Question

Big Brothers, Inc. borrows $267,999 from the bank at 18.16 percent per year, compounded annually, to purchase new machinery. This loan is to be repaid in equal annual installments at the end of each year over the next 10 years. How much will each annual payment be?
Round the answer to two decimal places.

Answer 1

Based on the amount borrowed and the interest per year, Big Brothers, Inc will pay an annual payment of $59,973.15.

How much will Big Brothers, Inc. pay annually?

This can be found by using the present value of an annuity formula because the annual payment will be constant and therefore like an annuity.

Formula is:

Present value of annuity = Annual payment x ( 1 - (1 + rate) ^ -number of periods) / rate

Solving gives:

267,999 = Amount x ( 1 - ( 1 + 18.16%)⁻¹⁰) / 18.16%

267,999 = Amount x 4.46865

Amount = 267,999 / 4.46865

= $59,973.15

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