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Ian loaned his friend $20,000 to start a new business. He considers this loan to be an investment, and therefore requires his friend to pay him an interest rate of 6% on the loan. He also expects his friend to pay back the loan over the next four years by making annual payments at the end of each year. Ian texted and asked that you help him calculate the annual payments that he should expect to receive so that he can recover his initial investment and earn the agreed-upon 6% on his investment.

Required:
Calculate the annual payment.

Respuesta :

fichoh

Answer: $5,771.83

Explanation:

Given the following :

Present value (PV) = $20,000

Interest rate (r) = 6% = 0.06

Period (n) = 4 years

Annual payment (C) =?

PV = C * [(1 - (1 + r)^-n) / r]

20,000 = C * [(1 - (1 + 0.06)^-4) / 0.06]

20,000 = C * [(1 - (1.06)^-4) / 0.06]

20,000 = C * [(1 - 0.7920936) / 0.06]

20,000 = C * (0.2079064) / 0.06

20,000 = C * 3.4651066

Divide both sides by 3.4651066

20,000 / 3.4651066 = (3.4651066 * C) / 3.4651066

5771.8280 = C

Hence, the yearly cash flow = $5,771.83