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 please select the best answer from the choices provided a b c d

Answer 1

The interest that Niki paid in total will b A $39,695.48

what will be the interest paid by Nikki?

We will use the formula of amount for two monthly compounded

$A=\dfrac{P(1-(1+\dfrac{r}{t}^{-nt} )}{\dfrac{r}{t} }$

P is the periodic payment.

Here, A = $61,60

r = 0.0984

t = 6

n = 11 years  

By putting values in the formula we get,

$61600=\dfrac{P(1-(1+\dfrac{0.0984}{6} ^{-11\times6} )}{\dfrac{0.0984}{6} }$

$61600=\dfrac{P(1-(1+0.0164)^{-66}}{0.0164}$

$1010.24=P(1-0.341769)$

$1010.24=0.658231\times P$

$P= 1534.78$

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

Now the total payment made by Niki = $11\times 6\times 1534.78=101295.48$

Hence, interest paid is = $101295.48-61600=39695.48$

Thus interest that Niki paid in total will b A $39,695.48

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