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Question 1104185: Luke’s luck changed, and he was able to enroll full-time again. He has become employed full-time and earns $40 per hour. Becoming employed full-time will help him repay the $35,000 he borrowed in direct student loans at 4.66%. Because all students who borrow direct loans are placed into the standard repayment plan when entering repayment by the Department of Education, Luke looked into the details. He realized the cost benefit and chose to remain in this plan, it is the shortest in length and students pay the least amount of interest. After doing some calculations, he estimated his monthly payment will be $365, which includes principal and interest. In order for Luke to be able to afford his repayment under the Standard plan comfortably, he will need to allocate 12% of his paycheck.
If Luke’s monthly payment is $365.44 (principal and interest) and it takes 10 years to pay back the loan, what is the total cost of the loan?
Found 2 solutions by Theo, Shin123:
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! there's a lot of fluff in this problem (extraneous information), but the question is simply telling you that the length of the loan is 10 years and is asking you what is the total value of the payments made on the loan.
since the payments are monthly, then monthly compounding is assumed.
therefore the length of the loan is assumed to be 10 * 12 = 120 months.
120 monthly payments of 365.44 = 43,852.8 total payments made.
that should the answer to the question and therefore, your solution.
to go a bit further, 35,000 of that was to repay the principal and 8,852 of that was to pay the interest.
it appears that all the necessary information was given to you, so all that you had to do was multiply the number of payments by the payment amount to get the total payment made.
that is, of course, unless i'm missing something, or simply misunderstanding what the problem is really asking you for.
i took the liberty of checking the figures given, which were:
present value of the loan is 35,000.
interest rate per year is 4.66%.
length of the loan is 10 years.
i assumed monthly compounding.
i used the TI-BA II Plus and entered:
N = 120
I/Y = 4.66/12
PV = 35000
FV = 0
i then had the calculator compute PMT for me.
the calculator told me that PMT (the monthly payment) was 365.4399, which i then rounded to 365.44, confirming the information provided was correct.
Answer by Shin123(626)  (Show Source):
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