This document discusses compound interest and effective interest rates. It provides examples to illustrate the difference between nominal interest rates, which are stated as an annual percentage, and effective interest rates, which take into account interest compounding over time. The examples show that banking strategies that compound interest more frequently, such as quarterly instead of annually, result in higher overall returns. The document concludes with a formula for calculating effective annual interest rates when interest is compounded more frequently than annually.

1. COMPOUND INTEREST
By Professor Paul Hernandez
“Prof. H”

2. •Nominal Interest rate
- Interest Rate itself
•Effective Interest rate
- How much interest an investment earns overtime

3. Compound Interest Examples
Lets say you want to invest $500 into a bank in order to
build interest.
• Bank 1 pays 10% interest once a year
• Bank 2 pays 3% interest 4 times a year ( quarterly )

4. Bank 1 pays 10% interest once a year
• Future value = principal amount x ( 100% +10%)
• Future value = $500 x (110%)
• Future value = $500 x (1.10)
• Future value = $550
1.10 is the growth factor.
Nominal Interest

5. Bank 2 pays 3% interest 4 times a year
( quarterly )
• Future value = Principal Amount x (100% x 3%)
• Future value = Principal Amount x (1.03)
The interest is given quarterly, so four times a year. So
here’s how It will look
• Future value = $500 x(1.03 x 1.03 x 1.03 x 1.03 )
$500(1.03)^4
• Future value = $562.75
Effective interest rate

6. One more example!
Here is an another example of effective interest rate.
Ex. Determine the effective annual rate with a nominal rate
of 5%/year compounded monthly.
A=P(1+r/n)^nt
t = time/term
n= # of compoundings
P= Principal
r = nominal interest rate

7. Cont.
• t = 12
• n= 12
• P= 1
• r =0.05
A=P( 1 + 0.05/12)^12
1.0511 > 5.11% effective interest rate

8. GO FORTH AND MATH!