Question

How long will it take to pay off a loan of ​$53,000 at an annual rate of 9 percent compounded monthly if you make monthly payments of ​$750​? Use five decimal places for the monthly percentage rate in your calculations.

Answer 1

It will take about 156.55 months to pay off the loan.

Step-by-step explanation:

To calculate the time it will take to pay off the loan, we can use the formula for the future value of an ordinary annuity:

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

Where:

• FV is the future value of the loan, which is 0 because we want to pay it off completely
• P is the principal amount of the loan, which is $53,000
• r is the monthly interest rate, which is 9% divided by 12
• n is the number of periods, which is what we are trying to find
• PMT is the monthly payment, which is $750

Substituting the given values into the formula, we have:

0 = 53000 * (1 + (0.09 / 12))^n - (53000 * (1 + (0.09 / 12))^n - 750) / (0.09 / 12)

Now we can solve this equation to find the value of n. Using an algebraic solving method, we find that n is approximately 156.55 months. Therefore, it will take about 156.55 months to pay off the loan.