You 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 the problem, we need to find the present value of the expected cash flows and set them equal to the loan amount, and then solve for X. Using a financial calculator or spreadsheet, we can calculate:

PV = -25000 + 2500/(1+0.08)^1 + 5000/(1+0.08)^2 + 7500/(1+0.08)^3 + X/(1+0.08)^4 + X/(1+0.08)^5 + X/(1+0.08)^6 + X/(1+0.08)^7

Solving for X, we get X = $4,733.15, which is closest to choice C. Therefore, the answer is C.

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