Questions: If a person borrowed 500,000.00 at a 5.5% interest rate, how many months would it take to pay the loan off by making 3,000 payments?

Solution Steps

To solve this problem, we need to calculate the number of months required to pay off a loan using the given interest rate and monthly payment amount. This is a typical loan amortization problem. We will use the formula for the monthly payment of an amortizing loan and iterate to find the number of months needed to reduce the loan balance to zero.

To find the monthly interest rate, divide the annual interest rate by 12 and convert it to a decimal. Given an annual interest rate of \(5.5\%\), the monthly interest rate is: \[ \text{Monthly Interest Rate} = \frac{5.5}{12 \times 100} = 0.004583 \]

We need to determine how many months it will take to pay off the loan of \(\$500,000\) with monthly payments of \(\$3,000\). The loan balance is updated each month by adding the interest for that month and subtracting the monthly payment. This process is repeated until the loan balance is zero or less.

Starting with a principal of \(\$500,000\), we calculate the interest for each month and update the principal by subtracting the monthly payment. This process continues until the principal is paid off. The number of months required is found to be 316.

Final Answer