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:

The present value of the loan is $15,877

Explanation:

Solution

Given that:

A company must pay back the bank a single payment of = $20,000

The loan of interest = 8%

Present value of 1 = 8% for 3 years (0.7938)

Present value of annuity = 8% for 3 years (2.5771

Now,

We solve for the loan present value

which is,

$20,000 * 0.7938 = $15, 877

For the annuity (series of payment) = $20,000 * 2.5771

= $51,542