350 The banks's interest rate is 6.9% /a compounded monthly. About how many years will it take Jane to repay student loan. She plans to pay 1500 up front and then make monthly payments of her loan? [4]

## Step 1: Calculate the remaining loan amount.### Jane pays 350 - -1150 1150.## Step 2: Calculate the monthly interest rate.### The annual interest rate is . The monthly interest rate is .## Step 3: Determine the number of months to repay.### Let be the number of months. We use the formula for the future value of an annuity: , where is the future value (loan amount), is the monthly payment, is the monthly interest rate. In our case, . Simplifying, we get , which is . Taking the logarithm of both sides: .## Step 4: Convert months to years.### Since there are 12 months in a year, it will take Jane approximately years to repay the loan.