Question

A car loan of $17,346.09 is to be repaid with end-of-month payments of $425.15. 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 3 years and 11 months.

Step-by-step explanation:

To find the term of the loan, we can use the formula for the present value of an annuity:

PV = R * (1 - (1 + i)^(-n)) / i

Where PV is the loan amount, R is the monthly payment, i is the monthly interest rate, and n is the number of months.

In this case, PV is $17,346.09, R is $425.15, and i is 7%/12 = 0.583%. We can plug these values into the formula and solve for n.

Once we find the value of n, we can convert it into years and months by dividing n by 12 and taking the quotient as the number of years and the remainder as the number of months.

After doing the calculations, we find that the term of the loan is approximately 3 years and 11 months.