precalculus finance

Question

Find the periodic payment R required to amortize a loan of P dollars over t years with interest charged at the rate of r%/year compounded m times a year. (Round your answer to the nearest cent.)

P = 14,000, r = 4, t = 5, m = 2

Answer 1

A mortgage is exactly like an annuity, except that the borrower is the one paying out the regular, level payments to the lender. These fixed payments of R are based on a known present value (the loan amount P). The formula for present value of an annuity is

PV = R • [1 - (1 + i)^-n] / i, where n is the number of payments (and interest periods), and i is the interest earned per period.

Since m (which equals 2) is the number of compoundings per year, then we'll just divide the nominal rate r (which is 0.04) by 2 and consider that there are 10 interest periods (5 years times 2 periods per year).

So with these adjustments, we can plug in all the known values as follows:

14000 = R • (1 - 1.02^-10) / 0.02

14000 = 8.9826R

R = $1548.57