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Future Value of an Uneven Cashflow

Cash Flow

Cash Flow is money you get a little at a time.

Lets say, for example that for the next 4 years you will get the following cash flow.

Cash Flow
in 1 year	$ 320
in 2 years	$ 400
in 3 years	$ 650
in 4 years	$ 300

If you assume that the interest rate is 6.5% (which means that after you get the money, it will be invested and you will get 6.5% interest from it), how much money will you have in 4 years? In other words, what will the future value of this cash flow be?

Compounding Formula

FV=PV ( 1 + i / m)^mn

FV = Future Value
PV = Present Value
i = Interest rate (annual)
m = number of compounding periods per year
n = number of years

So you have to figure out the future value of each payment and then add them together.

First Payment

FV = PV ( 1 + i / m)^mn
FV = $320 (1 + .065 / 12 )^{12 X 3} (three years)
FV = $320 (1.0054167)³⁶
FV = $320 (1.2146716)
FV = $388.69

Second Payment

FV = PV ( 1 + i / m) ^mn
FV = $400 (1 + .065 / 12 )^{12 X 2} (two years)
FV = $400 (1.0054167)²⁴
FV = $400 (1.1384289)
FV = $455.37

Third Payment

FV = PV ( 1 + i / m)^mn
FV = $650 (1 + .065 / 12 )^{12 X 1} (one year)
FV = $650 (1.0054167)¹²
FV = $650 (1.0669719)
FV = $693.53

Fourth Payment - ( The payment is not compounded. There no time to earn interest)

FV = PV ( 1 + i / m)^mn
FV = $300 (1 + .065 / 12 )^{12 X 0}(0 years.)
FV = $300 (1.0054167)⁰
FV = $300 (1) (remember anything to the power of zero is 1)
FV = $300

Finally, add up all the numbers

$ 388.69
$ 455.37
$ 693.53
$ 300.00
----------
$1,837.59

So after 4 years, you will have $1,837.59. That is the future value of your uneven cash flow.