are negotiating to make a 7-year loan of $25,000 to Breck Inc.To repay you, Breck will pay $2,500 at the end of Year 1, $5,000 at the end of Year 2, and $7,500 at the end of Year 3, plus a fixed but currently unspecified cash flow, X, at the end of each year from Year 4 through Year 7.Breck is essentially riskless, so you are confident the payments will be made.You regard 8% as an appropriate rate of return on a low risk but illiquid 7-year loan.What cash flow must the investment provide at the end of each of the final 4 years, that is, what is X?
A)$4,271.67
B)$4,496.49
C)$4,733.15
D)$4,969.81
E)$5,218.30

Question

Quizplus · Accepted Answer

To solve for X, we need to find the present value of the cash flows and then set it equal to the loan amount of $25,000. Using a financial calculator, we can solve for X by inputting the following cash flows: 
Year 1: $2,500/(1.08^1) = $2,314.81
Year 2: $5,000/(1.08^2) = $4,290.22
Year 3: $7,500/(1.08^3) = $6,517.17
Year 4-7: X/(1.08^4) + X/(1.08^5) + X/(1.08^6) + X/(1.08^7) = X(2.589)
Total present value = $13,061.20 + X(2.589)
Setting this equal to the loan amount of $25,000: 
$25,000 = $13,061.20 + X(2.589)
X = $4,733.15, as shown in choice C.

Are Negotiating to Make a 7-Year Loan of $25,000 to Breck