Section
4.7:
Compound
Interest
Continuous Compounding Formula
P = Principal invested (original amount)
r = Interest rate
A  Pe rt
A = Amount after t years

t = # of years
Continuous Compounding Example
Justin has an initial investment of $2,500 at 3.85% compounded
continuously.
a) How much will Justin have
in his account after 12 years?
b) How long until Justin’s
investment reaches $4,000?
c) At what rate should Justin have invested his money if he
wanted his investment to triple in 20 years?
Continuous Compounding Practice
Chloë invests money in a bond trust that pays 7.2% interest
compounded continuously.
a) If she has $6,163.30 after 10 years, determine her initial
deposit.
b) How long will it take for Chloë’s bond trust to quadruple?
Computing the Effective Rate of Interest
Effective Rate of Interest: the equivalent annual simple interest
rate that would give you the same amount as compounding after
1 year.
Annual Rate
Effective
Rate
Annual Compounding
10%
10%
Semiannual Compounding
10%
10.25%
Quarterly Compounding
10%
10.381%
Monthly Compounding
10%
10.471%
Daily Compounding
10%
10.516%
Continuous Compounding
10%
10.517%
Computing the Effective Rate of Interest
On January 2, 2004, an investment is placed in an IRA that will
pay 8% per annum compounded continuously.
a) What is the effective rate of interest?
Section 4.7:
Compound
Interest
Homework #22:
Page 322
# 11, 21, 23, 31,
33, 39