Introduction to Finance

LEARNING ACTIVITY
Go to the Chase Bank website, http://www.chase.com. Under the “Savings Accounts and 
CDs” heading, go to “CDs” and identify the interest rates being paid on certifi cates of 
deposit (CDs) of various maturities and amounts.
9.2
Compounding to Determine 
Future Values
Compounding
is an arithmetic process whereby an initial value increases or grows at a 
com-
pound interest
rate over time to reach a value in the future. 
Compound interest
involves 
earning interest on interest in addition to interest on the principal or initial investment. To 
understand compounding, let’s assume that you leave the investment with a bank for more 
than one year. For example, the fi rst bank accepts your $1,000 deposit now, adds $80 at the 
end of one year, retains the $1,080 for the second year, and pays you interest at an 8 percent 
rate. The bank returns your initial deposit plus accumulated interest at the end of the second 
year. How much will you receive as a future value? 
In word terms, we have the following calculation:
Future value = Present value × [(1 + Interest rate) × (1 + Interest rate)]
For our two-year investment example, we have,
Future value = $1,000 × (1.08) × (1.08)
= $1,000 × 1.1664
= 
$1,166.40
= $1,166 (rounded)
A time line also can be used to illustrate this two-year example as follows: 
Begin:
Present Value $1,000 × 1.08 × 1.08
End:
$1,166.40 Future Value
Year
0
1
2
Thus, for a one-year investment, the return would be $1,080 ($1,000 × 1.08), which is 
the same as the return on a simple interest investment, as was previously shown. However, a 
two-year investment at an 8 percent compound interest rate will return $1,166.40, compared 
to $1,160 using an 8 percent simple interest rate.
The compounding concept also can be expressed in equation form as,
FV
n
= PV(1 + 
r
)
n
(9.1)