Question

A car loan of $23,419.59 is to be repaid with end-of-month payments of $398.29. If interest is 7% compounded monthly, how long is the term of the loan? State your answer in years and months (from 0 to 11 months).

It will require ___ year(s) and ___ month(s) to repay the loan.

Answer 1

The term of the loan is approximately 6 years and 1 month.

To find the term of the loan, we need to calculate the number of months it will take to repay the loan. We can use the formula for the future value of an ordinary annuity to solve for the time. The formula is:

FV = P * ((1 + r)^n - 1) / r

Where FV is the future value, P is the payment amount, r is the interest rate per period, and n is the number of periods.

Plugging in the given values:

FV = $23,419.59, P = $398.29, r = 7% / 12 = 0.00583333333

Let's solve for n:

$23,419.59 = $398.29 * ((1 + 0.00583333333)^n - 1) / 0.00583333333

Using algebraic methods, we find that n is approximately 72.77 months. Since the term of the loan is measured in years and months, we can divide 72.77 by 12 to get approximately 6 years and 1 month.