Question

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.

Answer 1

Niki pays $39,467 interest will he have paid in total.

Given that,

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.

We have to determine,

How much interest will he have paid in total?

According to the question,

The total interest will be paid is determined by,

$\rm PV = \dfrac{P\left(1 - (1 + \dfrac{r}{t})^{-nt}\right) }{ \dfrac{r}{t}}$

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.

Substitute all the values in the formula;

$\rm PV = \dfrac{P\left(1 - (1 + \dfrac{r}{t})^{-nt}\right) }{ \dfrac{r}{t}}\\\\\rm 61600 = \dfrac{P\left(1 - (1 + \dfrac{0.0984}{6})^{-11 \times 6}\right) }{ \dfrac{0.0986}{6}}\\\\61600 = \dfrac{P\left(1 - (1 + {0.0164})\right^{-66} }{0.0164}\\\\61600 = \dfrac{P\left(1 - (1.01640))^{-66}}{0.0164}\\\\ 61600 \times 0.0164 = P (1-0.341769)\\\\1010.24 = 0.658231P\\\\P = \dfrac{1010.24}{0.6582}\\\\P = 1534.78$

Therefore,

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.

Hence, Niki pays $39,467 interest will he have paid in total.

For more details about Interest rates refer to the link given below.

brainly.com/question/10302432