How to Calculate Loan Payment with APR of 14.9%

What is the formula to calculate the time needed to pay off a loan with an APR of 14.9% compounded monthly?

Given the total loan amount of $3,250, with monthly payments of $75 and an annual interest rate of 14.9% compounded monthly, how long will it take for you to pay off the loan?

Answer:

It will take approximately 62 months or about 5 years and 2 months to pay off the loan.

To calculate the time it would take for you to pay off the loan, you need to know the total loan amount, monthly payment, and the interest rate. Here, the total loan amount is $3,250, monthly payment is $75, and APR is 14.9% compounded monthly, which makes the monthly interest rate 1.24%.

Now use the formula for the number of months needed to pay off a loan: n = [-log(1-(r(P/L))] / log(1 + r) where r is the monthly interest rate, P is the principal amount of the loan, and L is the monthly loan payment.

When we plug in the numbers, we get: n = [-log(1 - (0.0124(3250/75)))] / log(1 + 0.0124) which simplifies to n = 61.89 months.

Since we can't have part of a month, it rounds up to 62 months. So, it will take approximately 62 months to pay off the loan with $75 monthly payments and a 14.9% interest rate compounded monthly.