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

The total amount of interest paid by Niki is  $39,695.48.

The loan is termed as the amount that is borrowed by the lender and is paid off back at some defined amount of interest.  

Computation of amount of interest to be paid by Niki:

 

The given information is:

 P is the periodic payment.

PV = $61,600

r = 0.0984

t = 6

n = 11 years  

$\begin{aligned}PV = \frac{P(1 - (1 +\frac{r}{t}^{nt}))}{\frac{r}{t}}\end{aligned}$

$\begin{aligned}61600 =\frac{P(1 - (1 +\frac{0.0984}{6}^{11\times6})}{\frac{0.0984}{6}}\end{aligned}$

$\begin{aligned}61600 =\frac{P(1 - (1 + 0.0164)^{66} )}{ 0.0164}\end{aligned}$

$61600\times0.0164 = P(1 - (1.0164)^{66} )$

$\begin{aligned}1010.24&=p\times(1-0.341769)\\1010.24&=0.658321\times p\\p&=\frac{1010.24}{0.658321}\\p&=1534.78\end{aligned}$

Niki pays $1534.78 every two months continuously for eleven years.

$\begin{aligned}\text{The total payment made by Niki} &= \text{Tenure Period} \times 6 \times \text{Amount of interest}\\\text{The total payment made by Niki}&=11\times6\times\ 1534.78\\\text{The total payment made by Niki}&= \ 101295.48\end{aligned}$

$\text{Interest paid} = \text{Total Payment} - PV\\\text{Interest paid} = 101295.48-61600\\\text{Interest paid} =\ 39,695.48$  

Therefore, the correct option is A.

To know more about the computation of interests, refer to the link below:

https://brainly.com/question/26051659