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Time Value of Money
Annuities
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Kinds of Interest Rates
Future Value of an Uneven Cash flow
Probability Distribution
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Disclaimer 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), compounded monthly, 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. 