You just borrowed $15,000 from a bank. If you pay $4,000 at the end of each year over the next 5 years, you will pay off the loan. What is the interest rate on the loan?

(4,000 * 5) - 15,000 = 5,000

I = prt

5,000 = 15,000 * r * 5

5,000 = 75,000 * r

100(5,000 / 75,000) = r

6.67% = r

This is not the answer that my professor gave in his solutions. He has an interest rate of 10.425% I know it is a present value annuity, just don't know how to set up and solve for the i, the unknown.

To determine the interest rate on the loan, we can use the concept of present value. The present value of an annuity formula can be used to find the interest rate.

First, let's break down the problem. You borrowed $15,000, and you will make payments of $4,000 at the end of each year for 5 years. The goal is to find the interest rate on the loan.

To use the present value formula, we need to understand that the future value of an annuity (the loan amount) is equal to the annuity payment multiplied by the present value interest factor.

The present value annuity factor can be calculated using the formula:

PVAF = (1 - (1 + r)^-n) / r

Where:
PVAF is the Present Value Annuity Factor
r is the interest rate per period
n is the number of periods

In this case, the future value is $15,000, the annuity payment is $4,000, and we want to find the interest rate, which is denoted by r. The number of periods (n) is 5 (since payments are made annually for 5 years).

Now, let's rearrange the formula to solve for r:

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

Where:
r is the interest rate per period
FV is the future value (loan amount)
PVAF is the Present Value Annuity Factor
PMT is the annuity payment
n is the number of periods

Plugging in the values, we get:

r = (1 - (15000 / (PVAF * 4000))) ^ (1/5) - 1

To find the value of PVAF, you can use a financial calculator or spreadsheet software. Alternatively, you can use a present value annuity factor table.

By substituting the value of PVAF into the above equation, you can calculate the interest rate (r) on the loan.