What is the value in year 6 of a $9,000 cash flow made in year 14 if interest rates are 7 percent in years "4 through 9" and increase to 10 percent after that?
A) $4,252.19
B) $4,417.46
C) $4,561.71
D) $45,798.53

Question

Quizplus · Accepted Answer

To find the value in year 6 of a $9,000 cash flow made in year 14, we need to discount the cash flow back to year 6 using the given interest rates. From year 14 to year 9, the interest rate is 10%, and from year 9 to year 6, the interest rate is 7%. First, discount the cash flow from year 14 to year 9:$$PV_{9} = \frac{FV}{(1 + r)^n} = \frac{9000}{(1 + 0.10)^5} = \frac{9000}{(1.10)^5}$$$$PV_{9} = \frac{9000}{1.61051} = 5586.95$$Then, discount it from year 9 to year 6 using the 7% interest rate:$$PV_{6} = \frac{PV_{9}}{(1 + r)^n} = \frac{5586.95}{(1 + 0.07)^3} = \frac{5586.95}{(1.07)^3}$$$$PV_{6} = \frac{5586.95}{1.225043} = 4561.71$$Therefore, the value in year 6 of a $9,000 cash flow made in year 14 is $4,561.71.

What Is the Value in Year 6 of a $9,000