Introduction to Finance

future 
value
of a savings amount or investment is its value at a specifi ed time or date in the future. 
In general word terms, we have,
Future value = Present value + (Present value × Interest rate)
Or,
Future value = Present value × (1 + Interest rate)
In our example, we have,
Future value = $1,000 + ($1,000 × 0.08)
= 
$1,080
Or,
Future value = $1,000 × 1.08
= 
$1,080
Let’s now assume that your $1,000 investment remains on deposit for two years but the 
bank pays only simple interest, which is interest earned only on the investment’s principal. In 
word terms, we have,
Future value = Present value × [1 + (Interest rate) × (number of periods)]
For our example, this becomes,
Future value = $1,000 × [1 + (0.08 × 2)]
= $1,000 × 1.16
= 
$1,160
Another bank will pay you a 10 percent interest rate on your money. Thus, you would receive 
$100 in interest ($1,000 × 0.10), or a return at the end of one year of $1,100 ($1,000 × 1.10) 
time value of money 
math of 
fi nance whereby a fi nancial return 
is earned over time by saving or 
investing money
present value 
value today of a 
savings amount or investment
future value 
value of a savings 
amount or an investment at a 
specifi ed time or date in the future

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9.2 Compounding to Determine Future Values
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from the second bank. While the $20 diff erence in return between the two banks ($1,100 
versus $1,080) is not great, it has some importance to most people. For a two-year deposit that 
pays 
simple interest 
annually, the diff erence increases to $40. The second bank would return 
$1,200 ($1,000 × 1.20) to you, versus $1,160 from the fi rst bank. If the funds were invested 
for ten years, we would accumulate $1,000 × [1 + (0.08 × 10)] or $1,800 at the fi rst bank. At 
the second bank, we would have $1,000 × [1 + (0.10 × 10)] or $2,000; a $200 diff erence. This 
interest rate diff erential between the two banks will become even more important when we 
introduce the concept of compounding.
Of course, today’s interest rates paid by banks and other fi nancial institutions are very 
low, in part, due to the Fed’s easy monetary policy during the 2007–08 fi nancial crisis and the 
2008–09 Great Recession, and since then, in an eff ort to stimulate economic growth.