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.

Answer 1

Step-by-step explanation:

The problem is related to present value.

The formula of present value is:

$PV=A\times[\frac{1-(1+\frac{i}{n})^{-t\times n} }{\frac{i}{n} }]$

In this case we need to first compute the amount paid every period then compute the total interest paid by subtracting the value of PV from the total payment made.

The information provided is:

PV = Loan amount (or Present value) = $61,600

A = Amount paid every period

i = Rate of interest = 9.84% compounded every 2 months

t = number of years = 11 years

n = number of payments made every year = 6

Compute the value of A as follows:

$PV=A\times[\frac{1-(1+\frac{i}{n})^{-t\times n} }{\frac{i}{n} }]\\61600=A\times[\frac{1-(1+\frac{0.0984}{6})^{-11\times6} }{\frac{0.0984}{6} }]\\61600=A\times[\frac{0.658231} {0.0164}]\\A=\frac{61600}{\frac{0.658231} {0.0164}} \\=1534.78$

This value is the payment made for 1 period.

Then in 11 years total payment made is:

$Total\ Payment =11\times6\times1534.78\\=101295.48$

Compute the interest paid as follows:

$Interest=Total\ Payment - PV\\ =101295.48-61600\\=39695.48$

Thus, the total interest paid by Niki is $39,695.48.

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Answer 2

Answer:

A) $39,695.48

Step-by-step explanation:

the person above is correct and better at explaining :)