
Quantitative Methods of Evaluating Businesses and Investments  Time Value of Money
In addition to being able to understand the financial statement, IAs must also have the ability to estimate the value of an investment in the future.
Future Value
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:
P_{n} = P_{0}(1+r)^{n}P_{n}is future value of P_{0}P_{0} 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.
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.
P_{n} = $10,000(1 + .09)^{10} = $23,674
Example 2  If interest is compounded monthly, the future value (P_{n}) is $24,514.
P_{n} = $10,000(1 + .09/12)^{120} = $24,514
Present Value
As part of your investment planning, you might also need to calculate the present value of investments. For example, if your clients want to retire with $1 million in their investment accounts, it would be useful to know how much they need to save each year to reach that goal.
You can simply reverse the future value formula like this:
P_{0 = }P_{n } (1+ r)^{ n} P_{n }= $23,674 P_{0} is the present value of P_{n}n = 10 years r = 9% 
Example: How much would somebody need to invest now if they wish to have $23,674 10 years from now based on a return of 9% compounded annually?
P_{0 }= $23,674 = $10,000
(1+ .09)^{ 10}
Exam Tips and Tricks A typical time value of money question will look something like this: 
 Internal rate of return
 Present value
 Expected return
 Future value
Rates of Return  Internal Rate of ReturnThe correct answer is "d"  the ending value of the investment is known as the future value.
P_{n }= $10,000(1+.06/12)^{120 }= $18,194
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