Question
The Scenario    
You are a financial planner who is investigating the options for a 45 year old man who wishes to have enough money to retire by the time he is 65. His current financial arrangements are as follows:
• He is paying off a mortgage on the property he lives in. The payments are currently $3,500 at the end of each month, which is enough to have the property paid off exactly in 10 years at the current interest rate of 4% p.a. effective.
• His salary has just been increased to $180,000 p.a., which is taxed at a rate of 30% before being paid to him. This is currently being paid on a monthly basis at the same time as the mortgage payment is due (i.e. at the end of each month).
• Currently each month, $3,500 of the net salary is going towards the mortgage, $3,500 is being used in expenses and any additional amount is being invested in a bank account earning 3% p.a. compounded monthly. These payments are being made on the same day the net salary is received.
• The current bank account balance is $100,000.
• He expects his expenses to increase by 0.4% each month, including next month (i.e. the expense at the end of the 1st month will be 3500 × 1.004).
• He expects his salary to increase at a rate of 5% p.a. going forward. This increase is processed on a yearly basis, with the next increase to occur after 12 further salary payments at the recently increased rate.
• Interest income in the bank account is taxed at a rate of 20% immediately on the interest income earned each month.
• He intends to live in his home when he is retired and live off the proceeds of his bank account in retirement.

a) Calculate the expected amount the man will have in his bank account at age 65 under the basis above. Assume all interest rates remain constant.
The first thing you notice about this man’s financial affairs is that it would most likely be beneficial for him to pay off the mortgage as quickly as possible. This would involve closing the bank account down immediately and making a lump sum contribution to the home loan, and then continuing the $3,500 per month repayments until the loan is paid off. Again any additional amount of salary not used is credited to the bank account (which starts from a balance of zero).
b) Calculate how much more the man will have at age 65 if he takes this approach.
The client mentions to you he is extremely risk averse and does not want to invest in anything where the cash-flows aren’t known in advance. Based on this you decide to only recommend fixed interest securities, with the intention of investigating the impact of investing the current bank account balance in these securities.
Two options which you are considering are as follows:
Bond A – A zero coupon bond redeemable in 20 years with a gross yield of 7.5% p.a. effective.
Bond B – Pays half yearly coupons of 8% p.a. Redemption is at par on any coupon date between 15 and 20 years from now at the decision of the issuer. This bond has a minimum gross yield of 10% p.a. effective.
c) Assuming the man invests in either Bond A or Bond B (but not both at the same time); calculate the nominal amount of each bond which can be purchased using the current bank account balance of $100,000.
Should the client decide to invest in one of the bonds above, you decide to recommend that the mortgage continue to be paid off with the $3,500 per month for 10 years. You also discover that the government is planning to increase taxes on higher salaries. Any salary over $250,000 p.a. will be taxed at 40% (i.e. the first $250,000 p.a. of salary is taxed at 30%, the amount over $250,000 p.a. is taxed at 40% - tax is paid at a constant rate each month during each year assuming that the monthly salary is to be earned over the whole year). The client is also subject to a tax of 20% on coupons and 30% on capital gains, payable immediately it is incurred, with coupons to be invested in the bank account when they are received. The gross yields of the bonds are unchanged.
d) For both bond purchase options, calculate how much money the man will have in the bank account at age 65. Assume that Bond B is redeemed at the most advantageous date for the issuer.
e) Which of the four alternatives discussed above should the man choose such that he has the largest bank balance at the age of 65? Give a short explanation for your answer.
Solution Preview

These solutions may offer step-by-step problem-solving explanations or good writing examples that include modern styles of formatting and construction of bibliographies out of text citations and references.
Students may use these solutions for personal skill-building and practice.
Unethical use is strictly forbidden.

Summary:

Alternative
1 No Bonds. Beginning bank acct balance is 100k. Mortgage to be paif off in 10 years. Salaries
exceeding 250k is taxed at 40%.
2 No Bonds. Beginning bank acct balance is zero to payoff part of mortgage. Salaries exceeding
250k is taxed at 40%.
3 The 100k is invested in Bond A.
4 The 100k is invested in Bond B.

Balance at age 65
1 1,855,562.17
2 1,878,584.38
3 2,021,381.76 best choice
4 1,891,110.51

All things equal, it is advantageous to invest in a bond whose return is greater than the cost of the mortgage, than to payoff the mortgage.
Also, Bond A looks more advantageous than Bond B since the coupons in Bond B are eaten away by the coupon taxes.
This is only a preview of the solution.
Please use the purchase button to see the entire solution.
By purchasing this solution you'll be able to access the following files:
Solution.xlsx
Purchase Solution
$23.00 $11.5
Google Pay
Amazon
Paypal
Mastercard
Visacard
Discover
Amex
View Available Business Tutors 529 tutors matched
Ionut
(ionut)
Hi! MSc Applied Informatics & Computer Science Engineer. Practical experience in many CS & IT branches.Research work & homework
5/5 (5,654+ sessions)
2 hours avg response
Leo
(Leo)
Hi! I have been a professor in New York and taught in a math department and in an applied math department.
4.9/5 (5,652+ sessions)
2 hours avg response
Pranay
(math1983)
Ph.D. in mathematics and working as an Assistant Professor in University. I can provide help in mathematics, statistics and allied areas.
4.6/5 (5,512+ sessions)
1 hour avg response

Similar Homework Solutions

8.1.0PHP Version454msRequest Duration45MBMemory UsageGET college-homework-library/{category}/{subject}/{id}Route
    • Booting (269ms)time
    • Application (186ms)time
    • 1 x Booting (59.14%)
      269ms
      1 x Application (40.86%)
      186ms
      • Illuminate\Routing\Events\Routing (1.05ms)
      • Illuminate\Routing\Events\RouteMatched (488μs)
      • Illuminate\Foundation\Events\LocaleUpdated (2.42ms)
      • eloquent.booting: App\Models\HomeworkLibrary\HomeworkLibrary (148μs)
      • eloquent.booted: App\Models\HomeworkLibrary\HomeworkLibrary (153μs)
      • Illuminate\Database\Events\ConnectionEstablished (806μs)
      • Illuminate\Database\Events\StatementPrepared (27.95ms)
      • Illuminate\Database\Events\QueryExecuted (973μs)
      • eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibrary (97μs)
      • eloquent.booting: App\Models\Subject (100μs)
      • eloquent.booted: App\Models\Subject (44μs)
      • Illuminate\Database\Events\StatementPrepared (1.6ms)
      • Illuminate\Database\Events\QueryExecuted (893μs)
      • eloquent.retrieved: App\Models\Subject (96μs)
      • eloquent.booting: App\Models\HomeworkLibrary\HomeworkLibraryFile (111μs)
      • eloquent.booted: App\Models\HomeworkLibrary\HomeworkLibraryFile (94μs)
      • Illuminate\Database\Events\StatementPrepared (679μs)
      • Illuminate\Database\Events\QueryExecuted (818μs)
      • eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibraryFile (65μs)
      • eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibraryFile (13μs)
      • eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibraryFile (8μs)
      • eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibraryFile (6μs)
      • eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibraryFile (6μs)
      • eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibraryFile (5μs)
      • eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibraryFile (5μs)
      • eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibraryFile (6μs)
      • eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibraryFile (5μs)
      • eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibraryFile (5μs)
      • eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibraryFile (4μs)
      • eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibraryFile (5μs)
      • eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibraryFile (5μs)
      • eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibraryFile (5μs)
      • eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibraryFile (5μs)
      • eloquent.booting: App\Models\SubjectCat (457μs)
      • eloquent.booted: App\Models\SubjectCat (42μs)
      • Illuminate\Database\Events\StatementPrepared (691μs)
      • Illuminate\Database\Events\QueryExecuted (1.07ms)
      • eloquent.retrieved: App\Models\SubjectCat (79μs)
      • Illuminate\Cache\Events\CacheHit (17.19ms)
      • Illuminate\Cache\Events\CacheMissed (249μs)
      • Illuminate\Database\Events\StatementPrepared (993μs)
      • Illuminate\Database\Events\QueryExecuted (2.71ms)
      • eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibrary (83μs)
      • eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibrary (16μs)
      • eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibrary (9μs)
      • eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibrary (7μs)
      • eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibrary (7μs)
      • eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibrary (5μs)
      • Illuminate\Database\Events\StatementPrepared (719μs)
      • Illuminate\Database\Events\QueryExecuted (870μs)
      • eloquent.retrieved: App\Models\Subject (72μs)
      • Illuminate\Cache\Events\KeyWritten (875μs)
      • Illuminate\Database\Events\StatementPrepared (2.62ms)
      • Illuminate\Database\Events\QueryExecuted (3.3ms)
      • Illuminate\Database\Events\StatementPrepared (10.13ms)
      • Illuminate\Database\Events\QueryExecuted (1.89ms)
      • Illuminate\Database\Events\StatementPrepared (903μs)
      • Illuminate\Database\Events\QueryExecuted (1.39ms)
      • eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibraryFile (62μs)
      • Illuminate\Cache\Events\CacheHit (763μs)
      • creating: homework.show (277μs)
      • composing: homework.show (122μs)
      • creating: components.breadcrumbs (316μs)
      • composing: components.breadcrumbs (124μs)
      • Illuminate\Database\Events\StatementPrepared (2.61ms)
      • Illuminate\Database\Events\QueryExecuted (2.58ms)
      • eloquent.retrieved: App\Models\SubjectCat (84μs)
      • Illuminate\Cache\Events\CacheHit (2.54ms)
      • Illuminate\Cache\Events\CacheHit (140μs)
      • Illuminate\Cache\Events\CacheHit (160μs)
      • Illuminate\Cache\Events\CacheHit (114μs)
      • Illuminate\Cache\Events\CacheHit (126μs)
      • Illuminate\Cache\Events\CacheHit (105μs)
      • Illuminate\Cache\Events\CacheHit (117μs)
      • Illuminate\Cache\Events\CacheHit (103μs)
      • Illuminate\Cache\Events\CacheHit (1.87ms)
      • Illuminate\Cache\Events\CacheHit (265μs)
      • Illuminate\Cache\Events\CacheHit (160μs)
      • Illuminate\Cache\Events\CacheHit (114μs)
      • Illuminate\Cache\Events\CacheHit (125μs)
      • Illuminate\Cache\Events\CacheHit (112μs)
      • Illuminate\Cache\Events\CacheHit (152μs)
      • Illuminate\Cache\Events\CacheHit (116μs)
      • Illuminate\Cache\Events\CacheHit (492μs)
      • Illuminate\Cache\Events\CacheHit (146μs)
      • Illuminate\Cache\Events\CacheHit (136μs)
      • Illuminate\Cache\Events\CacheHit (113μs)
      • Illuminate\Cache\Events\CacheHit (127μs)
      • Illuminate\Cache\Events\CacheHit (130μs)
      • Illuminate\Cache\Events\CacheHit (141μs)
      • Illuminate\Cache\Events\CacheHit (125μs)
      • Illuminate\Cache\Events\CacheHit (129μs)
      • Illuminate\Cache\Events\CacheHit (101μs)
      • Illuminate\Cache\Events\CacheHit (115μs)
      • Illuminate\Cache\Events\CacheHit (98μs)
      • Illuminate\Cache\Events\CacheHit (134μs)
      • Illuminate\Cache\Events\CacheHit (112μs)
      • Illuminate\Cache\Events\CacheHit (3.5ms)
      • Illuminate\Cache\Events\CacheHit (164μs)
      • Illuminate\Cache\Events\CacheHit (148μs)
      • Illuminate\Cache\Events\CacheHit (130μs)
      • Illuminate\Cache\Events\CacheHit (139μs)
      • Illuminate\Cache\Events\CacheHit (112μs)
      • Illuminate\Cache\Events\CacheHit (130μs)
      • Illuminate\Cache\Events\CacheHit (102μs)
      • Illuminate\Cache\Events\CacheHit (115μs)
      • Illuminate\Cache\Events\CacheHit (99μs)
      • Illuminate\Cache\Events\CacheHit (113μs)
      • Illuminate\Cache\Events\CacheHit (99μs)
      • Illuminate\Cache\Events\CacheHit (112μs)
      • Illuminate\Cache\Events\CacheHit (97μs)
      • Illuminate\Cache\Events\CacheHit (127μs)
      • Illuminate\Cache\Events\CacheHit (110μs)
      • Illuminate\Cache\Events\CacheHit (120μs)
      • Illuminate\Cache\Events\CacheHit (100μs)
      • Illuminate\Cache\Events\CacheHit (498μs)
      • Illuminate\Cache\Events\CacheHit (146μs)
      • Illuminate\Cache\Events\CacheHit (133μs)
      • Illuminate\Cache\Events\CacheHit (133μs)
      • Illuminate\Cache\Events\CacheHit (132μs)
      • Illuminate\Cache\Events\CacheHit (109μs)
      • Illuminate\Cache\Events\CacheHit (132μs)
      • Illuminate\Cache\Events\CacheHit (103μs)
      • Illuminate\Cache\Events\CacheHit (121μs)
      • Illuminate\Cache\Events\CacheHit (98μs)
      • Illuminate\Cache\Events\CacheHit (120μs)
      • Illuminate\Cache\Events\CacheHit (99μs)
      • Illuminate\Cache\Events\CacheHit (114μs)
      • Illuminate\Cache\Events\CacheHit (98μs)
      • Illuminate\Cache\Events\CacheHit (126μs)
      • Illuminate\Cache\Events\CacheHit (108μs)
      • Illuminate\Cache\Events\CacheHit (122μs)
      • Illuminate\Cache\Events\CacheHit (2.56ms)
      • Illuminate\Cache\Events\CacheHit (186μs)
      • Illuminate\Cache\Events\CacheHit (129μs)
      • Illuminate\Cache\Events\CacheHit (135μs)
      • Illuminate\Cache\Events\CacheHit (114μs)
      • Illuminate\Cache\Events\CacheHit (128μs)
      • Illuminate\Cache\Events\CacheHit (301μs)
      • Illuminate\Cache\Events\CacheHit (151μs)
      • Illuminate\Cache\Events\CacheHit (115μs)
      • Illuminate\Cache\Events\CacheHit (779μs)
      • Illuminate\Cache\Events\CacheHit (162μs)
      • Illuminate\Cache\Events\CacheHit (142μs)
      • Illuminate\Cache\Events\CacheHit (114μs)
      • Illuminate\Cache\Events\CacheHit (129μs)
      • Illuminate\Cache\Events\CacheHit (111μs)
      • Illuminate\Cache\Events\CacheHit (125μs)
      • Illuminate\Cache\Events\CacheHit (111μs)
      • Illuminate\Cache\Events\CacheHit (1.4ms)
      • Illuminate\Cache\Events\CacheHit (138μs)
      • Illuminate\Cache\Events\CacheHit (137μs)
      • Illuminate\Cache\Events\CacheHit (114μs)
      • Illuminate\Cache\Events\CacheHit (131μs)
      • Illuminate\Cache\Events\CacheHit (112μs)
      • Illuminate\Cache\Events\CacheHit (132μs)
      • Illuminate\Cache\Events\CacheHit (102μs)
      • Illuminate\Cache\Events\CacheHit (130μs)
      • Illuminate\Cache\Events\CacheHit (3.1ms)
      • Illuminate\Cache\Events\CacheHit (178μs)
      • Illuminate\Cache\Events\CacheHit (125μs)
      • Illuminate\Cache\Events\CacheHit (148μs)
      • Illuminate\Cache\Events\CacheHit (197μs)
      • Illuminate\Cache\Events\CacheHit (123μs)
      • Illuminate\Cache\Events\CacheHit (519μs)
      • Illuminate\Cache\Events\CacheHit (137μs)
      • Illuminate\Cache\Events\CacheHit (100μs)
      • Illuminate\Cache\Events\CacheHit (196μs)
      • Illuminate\Cache\Events\CacheHit (112μs)
      • Illuminate\Cache\Events\CacheHit (133μs)
      • Illuminate\Cache\Events\CacheHit (105μs)
      • Illuminate\Cache\Events\CacheHit (126μs)
      • Illuminate\Cache\Events\CacheHit (98μs)
      • Illuminate\Cache\Events\CacheHit (137μs)
      • Illuminate\Cache\Events\CacheHit (110μs)
      • Illuminate\Cache\Events\CacheHit (124μs)
      • Illuminate\Cache\Events\CacheHit (108μs)
      • Illuminate\Cache\Events\CacheHit (119μs)
      • Illuminate\Cache\Events\CacheHit (97μs)
      • Illuminate\Cache\Events\CacheHit (158μs)
      • Illuminate\Cache\Events\CacheHit (117μs)
      • Illuminate\Cache\Events\CacheHit (618μs)
      • Illuminate\Cache\Events\CacheHit (111μs)
      • Illuminate\Cache\Events\CacheHit (119μs)
      • Illuminate\Cache\Events\CacheHit (100μs)
      • Illuminate\Cache\Events\CacheHit (5.84ms)
      • Illuminate\Cache\Events\CacheHit (159μs)
      • Illuminate\Cache\Events\CacheHit (135μs)
      • Illuminate\Cache\Events\CacheHit (109μs)
      • Illuminate\Cache\Events\CacheHit (122μs)
      • Illuminate\Cache\Events\CacheHit (102μs)
      • Illuminate\Cache\Events\CacheHit (117μs)
      • Illuminate\Cache\Events\CacheHit (102μs)
      • Illuminate\Cache\Events\CacheHit (113μs)
      • Illuminate\Cache\Events\CacheHit (151μs)
      • Illuminate\Cache\Events\CacheHit (126μs)
      • Illuminate\Cache\Events\CacheHit (100μs)
      • Illuminate\Cache\Events\CacheHit (4.15ms)
      • Illuminate\Cache\Events\CacheHit (185μs)
      • Illuminate\Cache\Events\CacheHit (155μs)
      • Illuminate\Cache\Events\CacheHit (109μs)
      • Illuminate\Cache\Events\CacheHit (4.31ms)
      • Illuminate\Cache\Events\CacheHit (157μs)
      • Illuminate\Cache\Events\CacheHit (132μs)
      • Illuminate\Cache\Events\CacheHit (105μs)
      • Illuminate\Cache\Events\CacheHit (115μs)
      • Illuminate\Cache\Events\CacheHit (99μs)
      • Illuminate\Cache\Events\CacheHit (220μs)
      • Illuminate\Cache\Events\CacheHit (133μs)
      • Illuminate\Cache\Events\CacheHit (352μs)
      • Illuminate\Cache\Events\CacheHit (122μs)
      • Illuminate\Cache\Events\CacheHit (123μs)
      • Illuminate\Cache\Events\CacheHit (100μs)
      • Illuminate\Cache\Events\CacheHit (115μs)
      • Illuminate\Cache\Events\CacheHit (99μs)
      • Illuminate\Cache\Events\CacheHit (113μs)
      • Illuminate\Cache\Events\CacheHit (97μs)
      • Illuminate\Cache\Events\CacheHit (113μs)
      • Illuminate\Cache\Events\CacheHit (98μs)
      • Illuminate\Cache\Events\CacheHit (112μs)
      • Illuminate\Cache\Events\CacheHit (97μs)
      • Illuminate\Cache\Events\CacheHit (111μs)
      • Illuminate\Cache\Events\CacheHit (96μs)
      • Illuminate\Cache\Events\CacheHit (152μs)
      • Illuminate\Cache\Events\CacheHit (105μs)
      • Illuminate\Cache\Events\CacheHit (114μs)
      • Illuminate\Cache\Events\CacheHit (111μs)
      • Illuminate\Cache\Events\CacheHit (118μs)
      • Illuminate\Cache\Events\CacheHit (99μs)
      • Illuminate\Cache\Events\CacheHit (142μs)
      • Illuminate\Cache\Events\CacheHit (110μs)
      • Illuminate\Cache\Events\CacheHit (124μs)
      • Illuminate\Cache\Events\CacheHit (106μs)
      • Illuminate\Cache\Events\CacheHit (119μs)
      • Illuminate\Cache\Events\CacheHit (97μs)
      • Illuminate\Cache\Events\CacheHit (113μs)
      • Illuminate\Cache\Events\CacheHit (96μs)
      • Illuminate\Cache\Events\CacheHit (111μs)
      • Illuminate\Cache\Events\CacheHit (96μs)
      • Illuminate\Cache\Events\CacheHit (109μs)
      • Illuminate\Cache\Events\CacheHit (3.41ms)
      • Illuminate\Cache\Events\CacheHit (206μs)
      • Illuminate\Cache\Events\CacheHit (120μs)
      • Illuminate\Cache\Events\CacheHit (126μs)
      • Illuminate\Cache\Events\CacheHit (105μs)
      • Illuminate\Cache\Events\CacheHit (211μs)
      • Illuminate\Cache\Events\CacheHit (155μs)
      • Illuminate\Cache\Events\CacheHit (131μs)
      • Illuminate\Cache\Events\CacheHit (106μs)
      • Illuminate\Cache\Events\CacheHit (142μs)
      • Illuminate\Cache\Events\CacheHit (114μs)
      • Illuminate\Cache\Events\CacheHit (124μs)
      • Illuminate\Cache\Events\CacheHit (108μs)
      • Illuminate\Cache\Events\CacheHit (121μs)
      • Illuminate\Cache\Events\CacheHit (100μs)
      • Illuminate\Cache\Events\CacheHit (113μs)
      • Illuminate\Cache\Events\CacheHit (98μs)
      • Illuminate\Cache\Events\CacheHit (124μs)
      • Illuminate\Cache\Events\CacheHit (96μs)
      • Illuminate\Cache\Events\CacheHit (109μs)
      • Illuminate\Cache\Events\CacheHit (94μs)
      • Illuminate\Cache\Events\CacheHit (117μs)
      • Illuminate\Cache\Events\CacheHit (99μs)
      • Illuminate\Cache\Events\CacheHit (159μs)
      • Illuminate\Cache\Events\CacheHit (104μs)
      • Illuminate\Cache\Events\CacheHit (127μs)
      • Illuminate\Cache\Events\CacheHit (121μs)
      • Illuminate\Cache\Events\CacheHit (134μs)
      • Illuminate\Cache\Events\CacheHit (106μs)
      • Illuminate\Cache\Events\CacheHit (121μs)
      • Illuminate\Cache\Events\CacheHit (98μs)
      • Illuminate\Cache\Events\CacheHit (111μs)
      • Illuminate\Cache\Events\CacheHit (97μs)
      • Illuminate\Cache\Events\CacheHit (110μs)
      • Illuminate\Cache\Events\CacheHit (97μs)
      • Illuminate\Cache\Events\CacheHit (108μs)
      • Illuminate\Cache\Events\CacheHit (95μs)
      • Illuminate\Cache\Events\CacheHit (110μs)
      • Illuminate\Cache\Events\CacheHit (95μs)
      • Illuminate\Cache\Events\CacheHit (4.4ms)
      • Illuminate\Cache\Events\CacheHit (162μs)
      • Illuminate\Cache\Events\CacheHit (630μs)
      • Illuminate\Cache\Events\CacheHit (113μs)
      • Illuminate\Cache\Events\CacheHit (121μs)
      • Illuminate\Cache\Events\CacheHit (103μs)
      • Illuminate\Cache\Events\CacheHit (114μs)
      • Illuminate\Cache\Events\CacheHit (99μs)
      • Illuminate\Cache\Events\CacheHit (112μs)
      • Illuminate\Cache\Events\CacheHit (99μs)
      • Illuminate\Cache\Events\CacheHit (115μs)
      • Illuminate\Cache\Events\CacheHit (97μs)
      • Illuminate\Cache\Events\CacheHit (142μs)
      • Illuminate\Cache\Events\CacheHit (228μs)
      • Illuminate\Cache\Events\CacheHit (161μs)
      • Illuminate\Cache\Events\CacheHit (105μs)
      • Illuminate\Cache\Events\CacheHit (114μs)
      • Illuminate\Cache\Events\CacheHit (98μs)
      • Illuminate\Cache\Events\CacheHit (112μs)
      • Illuminate\Cache\Events\CacheHit (99μs)
      • Illuminate\Cache\Events\CacheHit (141μs)
      • Illuminate\Cache\Events\CacheHit (109μs)
      • Illuminate\Cache\Events\CacheHit (129μs)
      • Illuminate\Cache\Events\CacheHit (99μs)
      • Illuminate\Cache\Events\CacheHit (116μs)
      • Illuminate\Cache\Events\CacheHit (98μs)
      • Illuminate\Cache\Events\CacheHit (111μs)
      • Illuminate\Cache\Events\CacheHit (104μs)
      • Illuminate\Cache\Events\CacheHit (2.69ms)
      • Illuminate\Cache\Events\CacheHit (136μs)
      • Illuminate\Cache\Events\CacheHit (129μs)
      • Illuminate\Cache\Events\CacheHit (107μs)
      • Illuminate\Cache\Events\CacheHit (118μs)
      • Illuminate\Cache\Events\CacheHit (103μs)
      • Illuminate\Cache\Events\CacheHit (116μs)
      • Illuminate\Cache\Events\CacheHit (100μs)
      • Illuminate\Cache\Events\CacheHit (114μs)
      • Illuminate\Cache\Events\CacheHit (98μs)
      • Illuminate\Cache\Events\CacheHit (113μs)
      • Illuminate\Cache\Events\CacheHit (97μs)
      • Illuminate\Cache\Events\CacheHit (130μs)
      • Illuminate\Cache\Events\CacheHit (104μs)
      • Illuminate\Cache\Events\CacheHit (117μs)
      • Illuminate\Cache\Events\CacheHit (96μs)
      • Illuminate\Cache\Events\CacheHit (111μs)
      • Illuminate\Cache\Events\CacheHit (335μs)
      • Illuminate\Cache\Events\CacheHit (190μs)
      • Illuminate\Cache\Events\CacheHit (123μs)
      • Illuminate\Cache\Events\CacheHit (130μs)
      • Illuminate\Cache\Events\CacheHit (117μs)
      • Illuminate\Cache\Events\CacheHit (128μs)
      • Illuminate\Cache\Events\CacheHit (116μs)
      • Illuminate\Cache\Events\CacheHit (120μs)
      • Illuminate\Cache\Events\CacheHit (108μs)
      • Illuminate\Cache\Events\CacheHit (163μs)
      • Illuminate\Cache\Events\CacheHit (186μs)
      • Illuminate\Cache\Events\CacheHit (157μs)
      • Illuminate\Cache\Events\CacheHit (127μs)
      • Illuminate\Cache\Events\CacheHit (131μs)
      • Illuminate\Cache\Events\CacheHit (104μs)
      • Illuminate\Cache\Events\CacheHit (117μs)
      • Illuminate\Cache\Events\CacheHit (100μs)
      • Illuminate\Cache\Events\CacheHit (128μs)
      • Illuminate\Cache\Events\CacheHit (101μs)
      • Illuminate\Cache\Events\CacheHit (127μs)
      • Illuminate\Cache\Events\CacheHit (96μs)
      • Illuminate\Cache\Events\CacheHit (112μs)
      • Illuminate\Cache\Events\CacheHit (95μs)
      • Illuminate\Cache\Events\CacheHit (116μs)
      • Illuminate\Cache\Events\CacheHit (99μs)
      • Illuminate\Cache\Events\CacheHit (126μs)
      • Illuminate\Cache\Events\CacheHit (103μs)
      • Illuminate\Cache\Events\CacheHit (118μs)
      • Illuminate\Cache\Events\CacheHit (99μs)
      • Illuminate\Cache\Events\CacheHit (305μs)
      • Illuminate\Cache\Events\CacheHit (114μs)
      • Illuminate\Cache\Events\CacheHit (126μs)
      • Illuminate\Cache\Events\CacheHit (101μs)
      • Illuminate\Cache\Events\CacheHit (116μs)
      • Illuminate\Cache\Events\CacheHit (99μs)
      • Illuminate\Cache\Events\CacheHit (115μs)
      • Illuminate\Cache\Events\CacheHit (99μs)
      • Illuminate\Cache\Events\CacheHit (253μs)
      • Illuminate\Cache\Events\CacheHit (133μs)
      • Illuminate\Cache\Events\CacheHit (124μs)
      • Illuminate\Cache\Events\CacheHit (98μs)
      • Illuminate\Cache\Events\CacheHit (113μs)
      • Illuminate\Cache\Events\CacheHit (163μs)
      • Illuminate\Cache\Events\CacheHit (131μs)
      • Illuminate\Cache\Events\CacheHit (101μs)
      • Illuminate\Cache\Events\CacheHit (131μs)
      • Illuminate\Cache\Events\CacheHit (100μs)
      • creating: site.layouts.app (361μs)
      • composing: site.layouts.app (18μs)
      • creating: components.canonical (336μs)
      • composing: components.canonical (152μs)
      • creating: components.open-graph (154μs)
      • composing: components.open-graph (48μs)
      • creating: site.headers.header (275μs)
      • composing: site.headers.header (50μs)
      • Illuminate\Cache\Events\CacheHit (1.92ms)
      • creating: components.footer (68μs)
      • composing: components.footer (106μs)
      • Illuminate\Cache\Events\CacheHit (628μs)
      • Illuminate\Cache\Events\CacheHit (188μs)
      • Illuminate\Cache\Events\CacheHit (165μs)
      • Illuminate\Cache\Events\CacheHit (125μs)
      • Illuminate\Cache\Events\CacheHit (115μs)
      • Illuminate\Cache\Events\CacheHit (146μs)
      • Illuminate\Cache\Events\CacheHit (140μs)
      • Illuminate\Cache\Events\CacheHit (355μs)
      • Illuminate\Cache\Events\CacheHit (214μs)
      • Illuminate\Cache\Events\CacheHit (121μs)
      • Illuminate\Cache\Events\CacheHit (158μs)
      • Illuminate\Cache\Events\CacheHit (205μs)
      • Illuminate\Cache\Events\CacheHit (251μs)
      • Illuminate\Cache\Events\CacheHit (216μs)
      • creating: components.forms.contact-us (246μs)
      • composing: components.forms.contact-us (144μs)
      • creating: components.forms.get-started (158μs)
      • composing: components.forms.get-started (75μs)
      • creating: components.forms.free-tool-download (142μs)
      • composing: components.forms.free-tool-download (74μs)
      • creating: components.forms.claim-free-worksheet (174μs)
      • composing: components.forms.claim-free-worksheet (71μs)
      • creating: components.forms.tutor-subscription-waitlist (141μs)
      • composing: components.forms.tutor-subscription-waitlist (85μs)
      • creating: components.forms.tutor-subscription-join (127μs)
      • composing: components.forms.tutor-subscription-join (68μs)
      • creating: components.forms.tutor-support (129μs)
      • composing: components.forms.tutor-support (74μs)
      • 321 x Illuminate\Cache\Events\CacheHit (22.43%)
        102ms
        10 x Illuminate\Database\Events\StatementPrepared (10.76%)
        48.89ms
        10 x Illuminate\Database\Events\QueryExecuted (3.63%)
        16.49ms
        1 x Illuminate\Foundation\Events\LocaleUpdated (0.53%)
        2.42ms
        1 x Illuminate\Routing\Events\Routing (0.23%)
        1.05ms
        1 x Illuminate\Cache\Events\KeyWritten (0.19%)
        875μs
        1 x Illuminate\Database\Events\ConnectionEstablished (0.18%)
        806μs
        1 x Illuminate\Routing\Events\RouteMatched (0.11%)
        488μs
        1 x eloquent.booting: App\Models\SubjectCat (0.1%)
        457μs
        1 x creating: site.layouts.app (0.08%)
        361μs
        1 x creating: components.canonical (0.07%)
        336μs
        1 x creating: components.breadcrumbs (0.07%)
        316μs
        1 x creating: homework.show (0.06%)
        277μs
        1 x creating: site.headers.header (0.06%)
        275μs
        1 x Illuminate\Cache\Events\CacheMissed (0.05%)
        249μs
        1 x creating: components.forms.contact-us (0.05%)
        246μs
        7 x eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibrary (0.05%)
        224μs
        16 x eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibraryFile (0.05%)
        210μs
        1 x creating: components.forms.claim-free-worksheet (0.04%)
        174μs
        2 x eloquent.retrieved: App\Models\Subject (0.04%)
        168μs
        2 x eloquent.retrieved: App\Models\SubjectCat (0.04%)
        163μs
        1 x creating: components.forms.get-started (0.03%)
        158μs
        1 x creating: components.open-graph (0.03%)
        154μs
        1 x eloquent.booted: App\Models\HomeworkLibrary\HomeworkLibrary (0.03%)
        153μs
        1 x composing: components.canonical (0.03%)
        152μs
        1 x eloquent.booting: App\Models\HomeworkLibrary\HomeworkLibrary (0.03%)
        148μs
        1 x composing: components.forms.contact-us (0.03%)
        144μs
        1 x creating: components.forms.free-tool-download (0.03%)
        142μs
        1 x creating: components.forms.tutor-subscription-waitlist (0.03%)
        141μs
        1 x creating: components.forms.tutor-support (0.03%)
        129μs
        1 x creating: components.forms.tutor-subscription-join (0.03%)
        127μs
        1 x composing: components.breadcrumbs (0.03%)
        124μs
        1 x composing: homework.show (0.03%)
        122μs
        1 x eloquent.booting: App\Models\HomeworkLibrary\HomeworkLibraryFile (0.02%)
        111μs
        1 x composing: components.footer (0.02%)
        106μs
        1 x eloquent.booting: App\Models\Subject (0.02%)
        100μs
        1 x eloquent.booted: App\Models\HomeworkLibrary\HomeworkLibraryFile (0.02%)
        94μs
        1 x composing: components.forms.tutor-subscription-waitlist (0.02%)
        85μs
        1 x composing: components.forms.get-started (0.02%)
        75μs
        1 x composing: components.forms.free-tool-download (0.02%)
        74μs
        1 x composing: components.forms.tutor-support (0.02%)
        74μs
        1 x composing: components.forms.claim-free-worksheet (0.02%)
        71μs
        1 x creating: components.footer (0.02%)
        68μs
        1 x composing: components.forms.tutor-subscription-join (0.01%)
        68μs
        1 x composing: site.headers.header (0.01%)
        50μs
        1 x composing: components.open-graph (0.01%)
        48μs
        1 x eloquent.booted: App\Models\Subject (0.01%)
        44μs
        1 x eloquent.booted: App\Models\SubjectCat (0.01%)
        42μs
        1 x composing: site.layouts.app (0%)
        18μs
      14 templates were rendered
      • 1x homework.showshow.blade.phpblade
      • 1x components.breadcrumbsbreadcrumbs.blade.phpblade
      • 1x site.layouts.appapp.blade.phpblade
      • 1x components.canonicalcanonical.blade.phpblade
      • 1x components.open-graphopen-graph.blade.phpblade
      • 1x site.headers.headerheader.blade.phpblade
      • 1x components.footerfooter.blade.phpblade
      • 1x components.forms.contact-uscontact-us.blade.phpblade
      • 1x components.forms.get-startedget-started.blade.phpblade
      • 1x components.forms.free-tool-downloadfree-tool-download.blade.phpblade
      • 1x components.forms.claim-free-worksheetclaim-free-worksheet.blade.phpblade
      • 1x components.forms.tutor-subscription-waitlisttutor-subscription-waitlist.blade.phpblade
      • 1x components.forms.tutor-subscription-jointutor-subscription-join.blade.phpblade
      • 1x components.forms.tutor-supporttutor-support.blade.phpblade
      uri
      GET college-homework-library/{category}/{subject}/{id}
      middleware
      web, utm.parameters
      controller
      App\Http\Controllers\HomeworkLibraryController@show
      namespace
      where
      as
      homework.show
      file
      app/Http/Controllers/HomeworkLibraryController.php:79-176
      10 statements were executed, 4 of which were duplicates, 6 unique. Show only duplicated53.51ms
      • Connection Establishedtwenty4_siteHomeworkLibraryController.php#91
        Backtrace
        • 13. app/Http/Controllers/HomeworkLibraryController.php:91
        • 14. vendor/laravel/framework/src/Illuminate/Routing/Controller.php:54
        • 15. vendor/laravel/framework/src/Illuminate/Routing/ControllerDispatcher.php:43
        • 16. vendor/laravel/framework/src/Illuminate/Routing/Route.php:260
        • 17. vendor/laravel/framework/src/Illuminate/Routing/Route.php:205
      • select * from `solutionslibrary` where `status` = 'published' and `price` > 0 and `solutionslibrary`.`id` = '20701' limit 1
        28.14mstwenty4_siteHomeworkLibraryController.php#97
        Bindings
        • 0: published
        • 1: 0
        • 2: 20701
        Backtrace
        • 16. app/Http/Controllers/HomeworkLibraryController.php:97
        • 17. vendor/laravel/framework/src/Illuminate/Routing/Controller.php:54
        • 18. vendor/laravel/framework/src/Illuminate/Routing/ControllerDispatcher.php:43
        • 19. vendor/laravel/framework/src/Illuminate/Routing/Route.php:260
        • 20. vendor/laravel/framework/src/Illuminate/Routing/Route.php:205
      • select * from `subjects` where `subjects`.`id` in (324)
        1.1mstwenty4_siteHomeworkLibraryController.php#97
        Backtrace
        • 21. app/Http/Controllers/HomeworkLibraryController.php:97
        • 22. vendor/laravel/framework/src/Illuminate/Routing/Controller.php:54
        • 23. vendor/laravel/framework/src/Illuminate/Routing/ControllerDispatcher.php:43
        • 24. vendor/laravel/framework/src/Illuminate/Routing/Route.php:260
        • 25. vendor/laravel/framework/src/Illuminate/Routing/Route.php:205
      • select * from `solutionslibrary_files` where `solutionslibrary_files`.`solutionlib_id` in (20701)
        970μstwenty4_siteHomeworkLibraryController.php#97
        Backtrace
        • 21. app/Http/Controllers/HomeworkLibraryController.php:97
        • 22. vendor/laravel/framework/src/Illuminate/Routing/Controller.php:54
        • 23. vendor/laravel/framework/src/Illuminate/Routing/ControllerDispatcher.php:43
        • 24. vendor/laravel/framework/src/Illuminate/Routing/Route.php:260
        • 25. vendor/laravel/framework/src/Illuminate/Routing/Route.php:205
      • select * from `subject_cats` where `subject_cats`.`id` = 4 limit 1
        1.3mstwenty4_siteHomeworkLibrary.php#201
        Bindings
        • 0: 4
        Backtrace
        • 20. app/Models/HomeworkLibrary/HomeworkLibrary.php:201
        • 26. app/Http/Controllers/HomeworkLibraryController.php:105
        • 27. vendor/laravel/framework/src/Illuminate/Routing/Controller.php:54
        • 28. vendor/laravel/framework/src/Illuminate/Routing/ControllerDispatcher.php:43
        • 29. vendor/laravel/framework/src/Illuminate/Routing/Route.php:260
      • select * from `solutionslibrary` where `id` <> 20701 and `subject` = 324 and `status` = 'published' and `price` > 0 order by RAND() limit 6
        2.93mstwenty4_siteHomeworkLibraryRepository.php#30
        Bindings
        • 0: 20701
        • 1: 324
        • 2: published
        • 3: 0
        Backtrace
        • 14. app/Repositories/HomeworkLibraryRepository.php:30
        • 15. vendor/laravel/framework/src/Illuminate/Cache/Repository.php:397
        • 16. vendor/laravel/framework/src/Illuminate/Cache/CacheManager.php:419
        • 18. app/Repositories/HomeworkLibraryRepository.php:39
        • 19. app/Http/Controllers/HomeworkLibraryController.php:139
      • select * from `subjects` where `subjects`.`id` in (324)
        1.06mstwenty4_siteHomeworkLibraryRepository.php#30
        Backtrace
        • 19. app/Repositories/HomeworkLibraryRepository.php:30
        • 20. vendor/laravel/framework/src/Illuminate/Cache/Repository.php:397
        • 21. vendor/laravel/framework/src/Illuminate/Cache/CacheManager.php:419
        • 23. app/Repositories/HomeworkLibraryRepository.php:39
        • 24. app/Http/Controllers/HomeworkLibraryController.php:139
      • select * from `solutionslibrary_files` where `solutionslibrary_files`.`solutionlib_id` = 20701 and `solutionslibrary_files`.`solutionlib_id` is not null and `publish` = 'question' order by `order` asc, `id` asc
        980μstwenty4_siteHomeworkLibrary.php#260
        Bindings
        • 0: 20701
        • 1: question
        Backtrace
        • 15. app/Models/HomeworkLibrary/HomeworkLibrary.php:260
        • 16. app/Transformers/HomeworkLibrary/HomeworkLibraryTransformer.php:58
        • 19. vendor/league/fractal/src/TransformerAbstract.php:128
        • 20. vendor/league/fractal/src/TransformerAbstract.php:107
        • 21. vendor/league/fractal/src/Scope.php:383
      • select * from `solutionslibrary_files` where `solutionslibrary_files`.`solutionlib_id` = 20701 and `solutionslibrary_files`.`solutionlib_id` is not null and `publish` = 'teaser' order by `order` asc, `id` asc
        11.07mstwenty4_siteHomeworkLibrary.php#260
        Bindings
        • 0: 20701
        • 1: teaser
        Backtrace
        • 15. app/Models/HomeworkLibrary/HomeworkLibrary.php:260
        • 16. app/Transformers/HomeworkLibrary/HomeworkLibraryTransformer.php:69
        • 19. vendor/league/fractal/src/TransformerAbstract.php:128
        • 20. vendor/league/fractal/src/TransformerAbstract.php:107
        • 21. vendor/league/fractal/src/Scope.php:383
      • select * from `solutionslibrary_files` where `solutionslibrary_files`.`solutionlib_id` = 20701 and `solutionslibrary_files`.`solutionlib_id` is not null and `publish` = 'solution' order by `order` asc, `id` asc
        1.69mstwenty4_siteHomeworkLibrary.php#260
        Bindings
        • 0: 20701
        • 1: solution
        Backtrace
        • 15. app/Models/HomeworkLibrary/HomeworkLibrary.php:260
        • 16. app/Transformers/HomeworkLibrary/HomeworkLibraryTransformer.php:80
        • 19. vendor/league/fractal/src/TransformerAbstract.php:128
        • 20. vendor/league/fractal/src/TransformerAbstract.php:107
        • 21. vendor/league/fractal/src/Scope.php:383
      • select * from `subject_cats` where `subject_cats`.`id` = 4 limit 1
        4.27mstwenty4_siteHomeworkLibrary.php#201
        Bindings
        • 0: 4
        Backtrace
        • 20. app/Models/HomeworkLibrary/HomeworkLibrary.php:201
        • 32. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:110
        • 33. vendor/laravel/framework/src/Illuminate/View/Engines/PhpEngine.php:58
        • 34. vendor/livewire/livewire/src/ComponentConcerns/RendersLivewireComponents.php:69
        • 35. vendor/laravel/framework/src/Illuminate/View/Engines/CompilerEngine.php:70
      App\Models\HomeworkLibrary\HomeworkLibraryFile
      16HomeworkLibraryFile.php
      App\Models\HomeworkLibrary\HomeworkLibrary
      7HomeworkLibrary.php
      App\Models\Subject
      2Subject.php
      App\Models\SubjectCat
      2SubjectCat.php
          _token
          yXlLDPLC5C0XRUFUiis8uji7Drj3R827jqyA5vxI
          utm_source
          direct
          redirectUrl
          /college-homework-library/Business/Mathematical-Finance/20701
          _previous
          array:1 [ "url" => "https://staging.dev.24houranswers.com/college-homework-library/Business/Mathem...
          _flash
          array:2 [ "old" => [] "new" => [] ]
          PHPDEBUGBAR_STACK_DATA
          []
          path_info
          /college-homework-library/Business/Mathematical-Finance/20701
          status_code
          200
          
          status_text
          OK
          format
          html
          content_type
          text/html; charset=UTF-8
          request_query
          []
          
          request_request
          []
          
          request_headers
          0 of 0
          array:21 [ "priority" => array:1 [ 0 => "u=0, i" ] "accept-encoding" => array:1 [ 0 => "gzip, deflate, br, zstd" ] "sec-fetch-dest" => array:1 [ 0 => "document" ] "sec-fetch-user" => array:1 [ 0 => "?1" ] "sec-fetch-mode" => array:1 [ 0 => "navigate" ] "sec-fetch-site" => array:1 [ 0 => "none" ] "accept" => array:1 [ 0 => "text/html,application/xhtml+xml,application/xml;q=0.9,image/avif,image/webp,image/apng,*/*;q=0.8,application/signed-exchange;v=b3;q=0.7" ] "user-agent" => array:1 [ 0 => "Mozilla/5.0 AppleWebKit/537.36 (KHTML, like Gecko; compatible; ClaudeBot/1.0; +claudebot@anthropic.com)" ] "upgrade-insecure-requests" => array:1 [ 0 => "1" ] "sec-ch-ua-platform" => array:1 [ 0 => ""Windows"" ] "sec-ch-ua-mobile" => array:1 [ 0 => "?0" ] "sec-ch-ua" => array:1 [ 0 => ""HeadlessChrome";v="129", "Not=A?Brand";v="8", "Chromium";v="129"" ] "cache-control" => array:1 [ 0 => "no-cache" ] "pragma" => array:1 [ 0 => "no-cache" ] "x-amzn-trace-id" => array:1 [ 0 => "Root=1-67b8e070-40e5115a159c2af8472aebd4" ] "host" => array:1 [ 0 => "staging.dev.24houranswers.com" ] "x-forwarded-port" => array:1 [ 0 => "443" ] "x-forwarded-proto" => array:1 [ 0 => "https" ] "x-forwarded-for" => array:1 [ 0 => "3.15.209.38" ] "content-length" => array:1 [ 0 => "" ] "content-type" => array:1 [ 0 => "" ] ]
          request_cookies
          []
          
          response_headers
          0 of 0
          array:5 [ "content-type" => array:1 [ 0 => "text/html; charset=UTF-8" ] "cache-control" => array:1 [ 0 => "no-cache, private" ] "date" => array:1 [ 0 => "Fri, 21 Feb 2025 20:22:08 GMT" ] "set-cookie" => array:2 [ 0 => "XSRF-TOKEN=eyJpdiI6IjYyUGxEWm1ncEFwZ1lrTzQwdzNXZWc9PSIsInZhbHVlIjoiRTFXb0g0S09uSWFBalh0T1V3V21PRExBNnNaMWp1THBOQ0tTeXV4TG1vakJYNWRzOFpmY1NicXdOZld1MitLU2F2QnBKcVE0NFU1cktVb040M0xQb2p6KzR3ZUVPdlZ1V0JPSDZkUjdwYVpqTVhCT1RXaXFzTDdnbHd1M2hyQ2EiLCJtYWMiOiIwZmUxZTRiYWZjYmVhMmQzMmE0MGEwYmRjYzA3M2E5N2JhYjgzYzE4MmZjNzIyMDlkNWJlMmM2NGI2ZTVjZjg0IiwidGFnIjoiIn0%3D; expires=Fri, 21 Feb 2025 22:22:08 GMT; Max-Age=7200; path=/; domain=.24houranswers.com; samesite=laxXSRF-TOKEN=eyJpdiI6IjYyUGxEWm1ncEFwZ1lrTzQwdzNXZWc9PSIsInZhbHVlIjoiRTFXb0g0S09uSWFBalh0T1V3V21PRExBNnNaMWp1THBOQ0tTeXV4TG1vakJYNWRzOFpmY1NicXdOZld1MitLU2F2QnBKc" 1 => "24houranswers_session=eyJpdiI6Ik9NcjlMTm12eUtaYVhOOUdtTHplUkE9PSIsInZhbHVlIjoidHF4cG9vNUZpaitaYXZZOU9zTUIveGdRNXBwK1cwTTJicUgvWDZDcW4zeWhwVEdsT3U4SllSY25HM0MyQnRITmM3NEhMT2lRNjRjcFo2Wm00YzRYa0Y4Q29kUE45cEk1dE5rSFZGQ2xwbHBtbU9raEJYUTg4T2tMZTU5aGs1UzEiLCJtYWMiOiI4ZTk4Yjg1Zjg3NTVlYTBkNWVhMzcyNzNmNTIxNzQ0MDU5MGU1ZDFlMzUzMDY3MzU5OTUzNDFmYmRiZmRmOWE0IiwidGFnIjoiIn0%3D; expires=Fri, 21 Feb 2025 22:22:08 GMT; Max-Age=7200; path=/; domain=.24houranswers.com; httponly; samesite=lax24houranswers_session=eyJpdiI6Ik9NcjlMTm12eUtaYVhOOUdtTHplUkE9PSIsInZhbHVlIjoidHF4cG9vNUZpaitaYXZZOU9zTUIveGdRNXBwK1cwTTJicUgvWDZDcW4zeWhwVEdsT3U4SllSY25HM0MyQn" ] "Set-Cookie" => array:2 [ 0 => "XSRF-TOKEN=eyJpdiI6IjYyUGxEWm1ncEFwZ1lrTzQwdzNXZWc9PSIsInZhbHVlIjoiRTFXb0g0S09uSWFBalh0T1V3V21PRExBNnNaMWp1THBOQ0tTeXV4TG1vakJYNWRzOFpmY1NicXdOZld1MitLU2F2QnBKcVE0NFU1cktVb040M0xQb2p6KzR3ZUVPdlZ1V0JPSDZkUjdwYVpqTVhCT1RXaXFzTDdnbHd1M2hyQ2EiLCJtYWMiOiIwZmUxZTRiYWZjYmVhMmQzMmE0MGEwYmRjYzA3M2E5N2JhYjgzYzE4MmZjNzIyMDlkNWJlMmM2NGI2ZTVjZjg0IiwidGFnIjoiIn0%3D; expires=Fri, 21-Feb-2025 22:22:08 GMT; domain=.24houranswers.com; path=/XSRF-TOKEN=eyJpdiI6IjYyUGxEWm1ncEFwZ1lrTzQwdzNXZWc9PSIsInZhbHVlIjoiRTFXb0g0S09uSWFBalh0T1V3V21PRExBNnNaMWp1THBOQ0tTeXV4TG1vakJYNWRzOFpmY1NicXdOZld1MitLU2F2QnBKc" 1 => "24houranswers_session=eyJpdiI6Ik9NcjlMTm12eUtaYVhOOUdtTHplUkE9PSIsInZhbHVlIjoidHF4cG9vNUZpaitaYXZZOU9zTUIveGdRNXBwK1cwTTJicUgvWDZDcW4zeWhwVEdsT3U4SllSY25HM0MyQnRITmM3NEhMT2lRNjRjcFo2Wm00YzRYa0Y4Q29kUE45cEk1dE5rSFZGQ2xwbHBtbU9raEJYUTg4T2tMZTU5aGs1UzEiLCJtYWMiOiI4ZTk4Yjg1Zjg3NTVlYTBkNWVhMzcyNzNmNTIxNzQ0MDU5MGU1ZDFlMzUzMDY3MzU5OTUzNDFmYmRiZmRmOWE0IiwidGFnIjoiIn0%3D; expires=Fri, 21-Feb-2025 22:22:08 GMT; domain=.24houranswers.com; path=/; httponly24houranswers_session=eyJpdiI6Ik9NcjlMTm12eUtaYVhOOUdtTHplUkE9PSIsInZhbHVlIjoidHF4cG9vNUZpaitaYXZZOU9zTUIveGdRNXBwK1cwTTJicUgvWDZDcW4zeWhwVEdsT3U4SllSY25HM0MyQn" ] ]
          session_attributes
          0 of 0
          array:6 [ "_token" => "yXlLDPLC5C0XRUFUiis8uji7Drj3R827jqyA5vxI" "utm_source" => "direct" "redirectUrl" => "/college-homework-library/Business/Mathematical-Finance/20701" "_previous" => array:1 [ "url" => "https://staging.dev.24houranswers.com/college-homework-library/Business/Mathematical-Finance/20701" ] "_flash" => array:2 [ "old" => [] "new" => [] ] "PHPDEBUGBAR_STACK_DATA" => [] ]