Question

Consider the following cash flows:

Year	Cash Flow
2		$	21,200
3			39,200
5			57,200

Assume an interest rate of 8 percent per year.

If today is Year 0, what is the future value of the cash flows five years from now? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)

Future value            $

If today is Year 0, what is the future value of the cash flows ten years from now? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)

Future value            $

Answer 1

To solve this problem, we must find the FV of each cash flow and add them. To find the FV of a lump sum, we use:

FV = PV(1 + r)^t

FV = $21,200(1.08)³ + $39,200(1.08)² + $57,200

FV = $129,628.77

Notice, since we are finding the value at Year 5, the cash flow at Year 5 is simply added to the FV of the other cash flows. In other words, we do not need to compound this cash flow.

To find the value in Year 10, we need to find the future value of this lump sum. Doing so, we find:

FV = PV(1 + r)^t

FV = $129,628.77(1.08)⁵

FV = 190,467.20