# Jones Co. borrowed money that is to be repaid in 12 years. So that the loan will be paid back at...

## Question:

Jones Co. borrowed money that is to be repaid in 12 years.

So that the loan will be paid back at end of the 12th year, the company invests $8,000 at end of each year at 5% compounded annually. Using the tables in the Business Math Handbook that accompanies the course textbook, determine the amount of the original loan. ## Loan Payments: Loan is often repaid through periodic payments of equal amounts. For example, mortgages are repaid through monthly payments of the same amount. These periodic payments are calculated such that the present value of the payments, discounted at the interest rate, is equal to the amount borrowed. ## Answer and Explanation: The amount of the original loan is$70,906.01.

The amount of the original loan is equal to the present value of the payments, which are an annuity. We can use the following formula to compute the present value of an annuity with periodic payment {eq}M {/eq} for {eq}T{/eq} periods, given periodic return {eq}r{/eq}:

• {eq}\displaystyle \frac{M(1 - (1 + r)^{-T})}{r} {/eq}

In this question, the annual payment is 8000, annual interest rate is 5%, and there are 12 payments. Applying the formula, the present value is:

• {eq}\displaystyle \frac{8000(1 - (1 + 5\%)^{-12})}{5\%} = 70,906.01 {/eq}