Question

You want to borrow $95,000 from your local bank to buy a new sailboat. You can afford to make monthly payments of $1,850, but no more. Assuming monthly compounding, what is the highest rate you can afford on a 60-month APR loan? (Do not round Intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16

Answer 1

To determine the highest rate you can afford on a 60-month APR loan, use the present value formula and rearrange it to solve for the interest rate. Plug in the given values and calculate the rate. The highest rate you can afford is 0.64707407%.

Step-by-step explanation:

To determine the highest rate you can afford on a 60-month APR loan, you can use the present value formula. First, calculate the present value (PV) using the monthly payment and the number of periods. PV = Payment * ((1 - (1 + R)^(-N)) / R), where R is the monthly interest rate and N is the number of periods. Rearrange the formula to solve for R. Take the natural logarithm of both sides (ln). R = (1 - (PV / Payment))^(1/N) - 1. Substitute the given values into the formula and solve for R. Convert R to a percentage by multiplying by 100.

In this case, PV = $95,000, Payment = $1,850, N = 60. Therefore, R = (1 - (95000 / 1850))^(1/60) - 1 = 0.0064707407. Multiplying by 100, the highest rate you can afford on a 60-month APR loan is 0.64707407%.