SOLUTION: I have arranged to borrow $18,000 from my parents toward a holiday. I will repay the loan over 6 years in equal year-end payments. If the interest rate is 9.7% p.a. compounding mon

Question 1161009: I have arranged to borrow $18,000 from my parents toward a holiday. I will repay the loan over 6 years in equal year-end payments. If the interest rate is 9.7% p.a. compounding monthly, my annual repayment is
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
nominal interest rate per year = 9.7% / 100 = .097
effective interest rate per year = (1 + .097/12) ^ 12 = 1.101430796 - 1 = .101430796 * 100 = 10.1430796%.
inputs to a financial calculator such as the one found at https://arachnoid.com/finance/index.html are:
present value = 18000
future value = 0
interest rate per time period = 10.1430796%
number of time periods = 6
payments are made at the end of each time period.
click on PMT and calculator tells you that the payments at the end of each year are 4150.28 for 6 years.
here's what the results look like.

since the money is compounded monthly, you have to use the effective annual interest rate per year rather than the nominal interest rate per year.
the effective interest rate is calculated by dividing 9.7% by 100 to get .097, dividing that by 12 to get the monthly interest rate, adding 1 to it, raising it to the 12th power, subtracting 1 from it, and then multiplying it by 100 to get the percent.
the percent is what this calculator requires.

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