document.write( "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 \n" ); document.write( "

Algebra.Com's Answer #785008 by Theo(13342) $\"\"$ $\"About$

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nominal interest rate per year = 9.7% / 100 = .097
\n" ); document.write( "effective interest rate per year = (1 + .097/12) ^ 12 = 1.101430796 - 1 = .101430796 * 100 = 10.1430796%.
\n" ); document.write( "inputs to a financial calculator such as the one found at https://arachnoid.com/finance/index.html are:
\n" ); document.write( "present value = 18000
\n" ); document.write( "future value = 0
\n" ); document.write( "interest rate per time period = 10.1430796%
\n" ); document.write( "number of time periods = 6
\n" ); document.write( "payments are made at the end of each time period.
\n" ); document.write( "click on PMT and calculator tells you that the payments at the end of each year are 4150.28 for 6 years.
\n" ); document.write( "here's what the results look like.
\n" ); document.write( "

\n" ); document.write( "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.
\n" ); document.write( "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.
\n" ); document.write( "the percent is what this calculator requires.\r
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