Question

A company must repay the bank a single payment of $20,000 cash in 3 years for a loan it entered into. The loan is at 8% interest compounded annually. The present value of 1 (single sum) at 8% for 3 years is 0.7938. The present value of an annuity (series of payments) at 8% for 3 years is 2.5771. The present value of the loan (rounded) is: Multiple Choice $15,876. $20,000. $25,195. $7,761. $51,542.

Answer 1

Answer:

Present Value of the loan = $19999.36 rounded off to $20000

Explanation:

The present value of loan will comprise of the present value of the principal amount of loan plus the present value of the interest that the loan will charge for the 3 year time period for which it is outstanding. As the interest payments are fixed and occur after equal intervals of time, they are considered an annuity.

To calculate the present value of the loan, we must discount the interest payments using the present value factor of annuity given in the question as 2.5771 and we must discount the principal to present value using the present value factor given in question as 0.7938.

We will first calculate the annual interest payment on loan.

Annual Interest payment = 20000 * 0.08 = 1600

Present value of the Interest payment - annuity = 1600 * 2.5771

Present value of the Interest payment - annuity = $4123.36

Present value of the Principal loan = 20000 * 0.7938

Present value of the Principal loan = $15876

Present Value of the loan = 15876 + 4123.36

Present Value of the loan = $19999.36 rounded off to $20000