SOLUTION: Rounding in the calculation of monthly interest rates is discouraged. Such rounding can lead to answers different from those presented here. For long-term loans, the differences ma
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Question 1118851: Rounding in the calculation of monthly interest rates is discouraged. Such rounding can lead to answers different from those presented here. For long-term loans, the differences may be pronounced.
Assume that you take out a $4000 loan for 30 months at 7% APR. How much of the first month's payment is interest? (Round your answer to the nearest cent.) Answer by Theo(13342) (Show Source):
the payment required per month would be 145.727629 per month.
the first payment is at the end of the first month.
the remaining balance at the beginning of the first month is 4000.
at the end of the first month, the interest is .07/12 * 4000 = 23.333333333.
the payment of 145.727629 is then made.
the principal part of the payment is 145.727629 - 23.3333333 = 122.3942957.
the remaining balance at the end of the first month is 4000 - 122.3942957 = 3877.605704.
as the number of months progress, the interest part is less and less and the principal part is more and more.
this can be seen in the following excel spreadsheet printout.
i used the TI-BA-II financial calculator to determine what the monthly payment needed to be.
i entered:
present value = 4000
future value = 0
payment is made at the end of the time period.
interest rate per time period is 7/12 = .58333333333.....
number of time periods = 30
i then had the calculator tell me what the required payment was.
the calculator said the required payment was 145.727629 at the end of each month.
you can see from the excel printout that the remaining balance at the end of the 30 month loan period is 0, as it should be.
