Question

The second and fifth cash flows in the following cash flow stream are missing. Both cash flows are the same (that is, CF2 = CF5). If the future value at the end of year 10 (that is, at t = 10) of this cash flow stream (these are the only cash flows in the cash flow stream) is $10,000 at a nominal annual interest rate of 8 percent, compounded semiannually, what is the amount of the missing cash flow?

Answer 1

Future value and present value are related as:

FV = PV x (1+r) ⁿ

r is the rate of interest and n is the number of period

Let the cash flow for year 2 and year 5 be C,

r = 8 % p.a. or 0.08/2 = 0.04 semiannually

$ 10,000 = C x (1.04)¹⁶ + C x (1.04)¹⁰

$ 10,000 = C x 1.872981245727 + C x 1.480244284918

$ 10,000 = C x (1.872981245727 + 1.480244284918)

$ 10,000 = C x 3.353225530646

C = $ 10,000 / 3.353225530646

C = $ 2,982.20322749209 or $ 2,982.20

Cash flow in year 2 and year 5 is $ 2,982.20