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8-18 Compound Interest CH 8]

greater than its present value.
FV > PV
Computing present value at compound interest answers this question: “What principal
invested now (or presently) at a given rate for a certain length of time will yield a specific
compounded amount?”

Present Value – Future Value Equations.
The present value equation that has a rate of return is:
Future value Numerator
Present Value =
n
(1 +r) Denominator
Where:
 FV = future value
 r = rate of return
 n = number of periods

How to Calculate Present Value
1. Input the future amount that you expect to receive in the numerator of the equation.
2. Determine the interest rate that you expect to receive between now and the future and plug the rate as a
decimal in place of "r" in the denominator.
3. Input the time period as the exponent "n" in the denominator. So, if you want to calculate the present
value of an amount you expect to receive in three years, you would plug the number three in for "n" in the
denominator.
4. Perform the arithmetic as indicated.

What Does Present Value Tell You?
FIAT CURRENCY:
Currency that a Present value is the concept that states an amount of money today purchases more than
government declares that same amount in the future. That is $1,000 today is not worth the same as $1,000 in the
to be legal tender, but future; that is, its purchasing power declines over time if it is not earning interest and
it is not backed by growing (the cause for the loss in purchasing power: inflation).
precious metals such Think about this: Receiving $1,000 today is worth more (it will purchase more goods and
as gold or silver. The
value of fiat money is services today) than $1,000 five years from now. Why? Two factors impact whether an
derived from the amount today is worth more than the same amount in the future—will the dollars today
relationship between possess the ability to purchase the same goods and services for the same amount of dollars
supply and demand five years from today. The answer is generally NO. The two reasons are (1) rising prices and
rather than the value (2) inflation. Inflation occurs when a government prints currency that is not backed by
of the material from precious metals such as gold or silver. This printing devalues the currency supply already on
which the money is hand, thus the government is creating fiat currency. The United States Federal Reserve
made. Value is also
decided by notes that you carry and use for transactions is fiat currency; it is NOT backed by precious
government and metals such as gold or gold.
keeps it as a medium
of exchange. Interest Rate or Rate of Return
Investing money with an expected interest rate, yielding a return on investment, should

grow at the expected rate of return over time and return to the investor a dollar amount and
purchasing power greater than when originally invested.
Consider an investor, who has $1,000 today, investing with an expected rate of return of
5% per year. The $1,000 today is certainly worth more than receiving $1,000 five years from
now. Let’s do the arithmetic and prove the case.
First let’s calculate the future value based on the information provided above.

The Future Value equation is:
The future value equation of an investment that has a rate of return is:
n
Future Value = Present Value x (1 + r )
Where:
 PV = present value
 r = rate of return
 n = number of periods

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