Question

Using a compound interest rate of 5.0% per period, what is the equivalent value at the end of period 5 (beginning of 6) of the cash flows given below?

Period	0	1	2	3	4	5	6	7
Cash Flow	200	400	400	400	600	600	-600	-1200

Answer 1

Here we will use the following formula:

FV = PV * (1 + r%)n

where, FV = Future value, PV = Present value, r = rate of interest = 5%, n= time period

For calculating the future value the given cash flows, we will calculate the future values of all the years and add them up. Now,putting the values in the above equation, we get,

FV = $200 * (1 + 5%)5 + $400 * (1 + 5%)4  + $400 * (1 + 5%)3 + $400 * (1 + 5%)2 + $600 * (1 + 5%)1

FV = $200 * (1 + 0.05)5 + $400 * (1 + 0.05)4  + $400 * (1 + 0.05)3 + $400 * (1 + 0.05)2 + $600 * (1 + 0.05)

FV = $200 * (1.05)5 + $400 * (1.05)4  + $400 * (1.05)3 + $400 * (1.05)2 + $600 * (1.05)

FV = ($200 * 1.2762815) + ($400 * 1.21550)  + ($400 * 1.157625) + ($400 * 1.1025) + $600 * (1.05)

FV = $255.2563125 + $486.2025 + $463.05 + $441 + $630

FV = $2275.51

So, value of the cash flows at the end of 5 years will be $2275.51