
Quantitative Methods  Time Value of Money
The concept of the time value of money takes into account that a dollar received today is worth more than a dollar received in the future. Financial planners must routinely calculate the future value of investments in order to help clients plan for goals such as retirement.
Future Value
When planning an investment strategy, it is 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:
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P_{n} = P_{0}(1+r)^{n}
P_{0} is the original amount invested
P_{n}is the future value of P_{0}
_{n}is the number of compounding periods (years, months, etc.)
r is the rate of interest
As the following examples illustrate, when you increase the frequency of compounding, you also increase the future value of your investment.
How much will an investment, (worth $10,000 today), be worth 10 years from now at a rate of 9%?
P_{0} = $10,000
P_{n }is the future value of P_{0}
_{n }= 10 years
r = 9%
Example 1: If interest is compounded annually, the future value (P_{n}) is $23,674.
10,000*(1.09)^{10*1 }= $23,674
Example 2: If interest is compounded monthly, the future value (P_{n}) is $24,514.
10,000*(1+(0.09/12)^{10*12} = $24,514
The same concepts can help you to calculate the amount needed today to reach the future value of a desired investment. For example, if a client wishes to retire with $1 million, it would be useful to know how much she needs to save each year to reach that goal.
You can simply reverse the future value formula to calculate the present value required:
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P_{0}_{ = }P_{n / }(1+ r)^{ n}
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Net Present Value (NPV)
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