Niki makes the same payment every two months to pay off his $61,600 loan. The loan has an interest rate of 9.84%, compounded eve
ry two months. If Niki pays off his loan after exactly eleven years, how much interest will he have paid in total? Round all dollar values to the nearest cent.
The question is an annuity question with the present value of the annuity given. The
present value of an annuity is given by PV = P(1 - (1 + r/t)^-nt) /
(r/t) where PV = $61,600; r = interest rate = 9.84% = 0.0984; t = number
of payments in a year = 6; n = number of years = 11 years and P is the
periodic payment. 61600 = P(1 - (1 + 0.0984/6)^-(11 x 6)) / (0.0984 / 6) 61600 = P(1 - (1 + 0.0164)^-66) / 0.0164 61600 x 0.0164 = P(1 - (1.0164)^-66) 1010.24 = P(1 - 0.341769) = 0.658231P P = 1010.24 / 0.658231 = 1534.78 Thus, Niki pays $1,534.78 every two months for eleven years. The total payment made by Niki = 11 x 6 x 1,534.78 = $101,295.48 Therefore, interest paid by Niki = $101,295.48 - $61,600 = $39,695.48
