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Time Value Of Money - Future Value And Compounding

There are two ways to calculate Future Value (FV):

1) For an asset with simple annual interest: = Original Investment x (1+(interest rate*number of years))

2) For an asset with interest compounded annually: = Original Investment x ((1+interest rate)^number of years) Consider the following examples:

1) $1000 invested for five years with simple annual interest of 10% would have a future value of $1,500.00.

2) $1000 invested for five years at 10%, compounded annually has a future value of $1,610.51.

When planning investment strategy, it's useful to be able to predict what an investment is likely to be worth in the future, taking the impact of compound interest into account. This formula allows you (or your calculator) to do just that:

Pn = P0(1+r)n
Pnis future value of P0
P0 is original amount invested
r is the rate of interest
n is the number of compounding periods (years, months, etc.)


Note in the example below that when you increase the frequency of compounding, you also increase the future value of your investment.

P0 = $10,000
Pn is the future value of P0
n = 10 years
r = 9%

Example 1- If interest is compounded annually, the future value (Pn) is $23,674.
Pn = $10,000(1 + .09)10 = $23,674

Example 2 - If interest is compounded monthly, the future value (Pn) is $24,514.
Pn = $10,000(1 + .09/12)120 = $24,514

To read more on this subject, see Continuously Compound Interest and Accelerating Returns With Continuous Compounding.

Present Value And Discounting


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