Compound interest is interest calculated on both the principal amount and on any interest that has already been earned over multiple periods. It is usually used for loans of more than one year. Compound interest is higher than simple interest because the interest earns interest. The compound interest formula can be used to calculate the future value (FV) of an investment given the present value (PV), interest rate per period (i), and number of compounding periods (n). An example calculates that $1500 compounded quarterly at 6.75% annually for 10 years results in a future value of $2929.

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2. Compound Interest
 Simple interest is generally used for loans of one year or less.
For loans of more than one year, the interest paid on the money
borrowed usually use compound interest.
 Compound interest is interest calculated not only on the original
principal, but also on any interest that has already been
earned.
…the calculation of interest over the life
of the loan or investment
Example: Principal + prior period interest = $1100.00
Interest is now calculated on $1100.00
Let’s assume that the interest rate is 10% pa.
Principal(Compounded) * 0.10 = $110.00
New P $1210.00 to start next period

3. Graphically
100
110
121
1000
1210
1331
1100
100 100
110
Time(Years)
0 1 2 3 4
Amount
$1000
110
Interes
t
Interes
t
100
Interes
t
133.1
Compounding
Period
Compounding
Period
Compounding
Period
Compounding
Period
Interes
t
121

4. Compounding Frequencies and Periods
Frequency No. per Year Period
Annually 1 1 year
Semiannually 2 6 months
Quarterly 4 3 months
Monthly 12 1 month
Daily 365 1 day
Period
Interest
Credited
Times Credited
per year
Rate per compounding
period
Annual year 1 R
Semiannual 6 months 2
Quarterly quarter 4
Monthly month 12
2
R
4
R
12
R

5. Compound Interest Formula
(n)Total Number of Period
Nominal or Annual Rate ( j )
Periodic Rate per period (i )
Number of compounding per year (m)
To Determine n
To Determine i
# of Compounding Frequencies p.a.(m)Time(Years)
Annual Interest Rate( j )
# of Compounding Frequencies p.a. (m)
*

6. Formula
…is the compounded amount and is the
FINAL amount of the loan or investment at the end of the
last period!
...is the value of a loan or investment
TODAY!
PV= Present Value(Principal)
i = rate per period
n = number of periods
FV = PV(1 + i)n
Where…

7. Example
 Find the amount to which $1500 will grow if compounded
quarterly at 6.75% interest for 10 years.
 Solution:
 Use future value formula
 Here PV = $1500, i = , n = 10  4
FV = 1500(1+0.016875)40
FV = 2929
FV = PV(1 + i)n
4
0675.0

8. The End
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