document.write( "Question 220275: The monthly payment on a 2-year loan is $500. The interest rate is 6.65% compunded monthly. What is the amount of the loan? \n" ); document.write( "

Algebra.Com's Answer #165421 by Theo(13342) $\"\"$ $\"About$

You can put this solution on YOUR website!
Formula for present value of a series of payments is:
\n" ); document.write( "PRESENT VALUE OF A PAYMENT
\n" ); document.write( " $\"+PV%28PMT%29+=+%28PMT+%2A+%281+-+%281+%2F+%281%2Bi%29%5En%29%29%2Fi%29+\"$
\n" ); document.write( "PV = present value
\n" ); document.write( "PMT = payment per time period
\n" ); document.write( "i = interest rate per time period
\n" ); document.write( "n = number of time periods
\n" ); document.write( "-----
\n" ); document.write( "6.55% per year compounded monthly is:
\n" ); document.write( "6.55/12 = .554166667% per month which equals a rate of:
\n" ); document.write( ".00554166667 per month.
\n" ); document.write( "Number of month is 2 years * 12 months = 24 months
\n" ); document.write( "payment is $500 per month.
\n" ); document.write( "-----
\n" ); document.write( "PV = what we want to find.
\n" ); document.write( "PMT = $500 per month
\n" ); document.write( "i = .00554166667 per month
\n" ); document.write( "n = 24 months
\n" ); document.write( "Formula becomes:
\n" ); document.write( " $\"+PV%28PMT%29+=+%28500+%2A+%281+-+%281+%2F+%281.0054166667%29%5E24%29%29%2F.0054166667%29+\"$
\n" ); document.write( "which equals: $11,224.28901
\n" ); document.write( "-----
\n" ); document.write( "The loan was $11,224.28901
\n" ); document.write( "The lender received $12,778.06 by the end of the loan (Future Value of a Series of Payments).
\n" ); document.write( "Principal was $11,224.29
\n" ); document.write( "Interest was $1,553.77 \n" ); document.write( "

\n" );