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 every 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. a. $39,695.48 b. $10,294.26 c. $3,126.29 d. $39,467.12

The present value (P) of an annuity is given by :

PV = P(1 - (1 + r/t)^-nt) / (r/t)

r = interest rate = 9.84% or 0.0984;

t = number of payments made in an year = 6;

n = number of years = 11 years

PV is the principle value or 61600

61600 = P(1 - (1 + 0.0984/6)^-(11 x 6)) / (0.0984 / 6)

61600 = P(1 - (1 + 0.0164)^-66) / 0.0164

61600 * 0.0164 = P(1 - (1.0164)^-66)

1010.24 = P(1 - 0.341769) = 0.658231P

P = 1010.24 / 0.658231 = 1534.78

Hence, Niki pays $1534.78 every two months for eleven years.

The total payment made by Niki = 11 * 6 * 1534.78 = $101295.48

Therefore, interest paid by Niki = 101295.48 - 61,600 = $39695.48

Hence, option A is the correct answer.

good luck on your studies! : )

david edward.