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 interest Niki have paid is $10,294.26. The correct option is B.

To find the total interest paid by Niki on his $61,600 loan with an interest rate of 9.84%, compounded every two months over eleven years, we can use the compound interest formula:

`\[ A = P \left(1 + (r)/(n)\right)^(nt) \]`

Where:

-
`\( A \)` is the total amount after time
`\( t \)`,

-
`\( P \)`is the principal amount (initial loan amount),

-
`\( r \)` is the annual interest rate (in decimal form),

-
`\( n \)` is the number of times interest is compounded per year,

-
`\( t \)` is the time in years.

The total interest paid
`(\( I \))` is then given by
`\( I = A - P \)`.

Given that the loan is compounded every two months,
`\( n = 6 \)` (since there are 12 months in a year), and the interest rate is 9.84% or
`\( r = 0.0984 \).`

`\[ A = 61600 \left(1 + (0.0984)/(6)\right)^(6 * 11) \]`

Calculate A and then find I by subtracting the principal $61,600. Round the answer to the nearest cent.

After calculations, the correct answer is:

b. $10,294.26