# Nanako takes out a loan of \$16,000 to buy a car. The loan has a simple interest rate of 8% per year. She pays back the loan at a fixed rate of \$250 per month. Find how long it will take for Nanako to repay the loan.

It will take approximately 9 years and 4 months to repay the loan.

Simple interest means that the interest is the same each year. In this case, `8 % ` of `\$ 1 6 , 0 0 0 ` is `0.08 * 1 6 , 0 0 0 = 8 * 1 6 0 = 1 , 2 8 0 ( \$ )...

Start your 48-hour free trial to unlock this answer and thousands more. Enjoy eNotes ad-free and cancel anytime.

Simple interest means that the interest is the same each year. In this case, `8 % ` of `\$ 1 6 , 0 0 0 ` is `0.08 * 1 6 , 0 0 0 = 8 * 1 6 0 = 1 , 2 8 0 ( \$ ) ` per year. The quicker the loan is paid, the smaller is the total interest.

This way, if the entire loan will be repaid in `n ` years, the interest paid will be `1 , 2 8 0 n ` dollars. Of course, the principal amount of `\$ 1 6 , 0 0 0 ` must be repaid also, so the total sum is `1 , 2 8 0 n + 1 6 , 0 0 0 ` dollars.

Each month, Nanako pays `\$ 2 5 0 , ` which means `\$ 3 , 0 0 0 ` a year. In `n ` years, she'll pay `3 , 0 0 0 n ` dollars, so we get an equation for `n . `

`3 , 0 0 0 n = 1 , 2 8 0 n + 1 6 , 0 0 0 .`

To solve: `1 , 7 2 0 n = 1 6 , 0 0 0 , ` `1 7 2 n = 1 , 6 0 0 , ` `4 3 n = 4 0 0 . ` So, `n = ( 4 0 0 ) / ( 4 3 ) approx 9 . 3 ` (years), which is about 9 years and 4 months.

Last Updated by eNotes Editorial on