136 Chapter 3 Compound Interest
Topic Key Ideas, Formulas, and Techniques Example(s)
Compound Interest with
“Messy” Terms, pp. 108–109- n in the compound interest formula must be the
number of time periods - The term must be converted to the same time
units as the compounding.
Nigel deposited $4,265.97
in a savings account paying
3.6% compounded daily. He
closed the account 3 years,
7 months, and 17 days later.
How much did he have
when he closed it? (Example
3.2.10)Effective Interest Rates, p. 117 • The effective interest rate for a given nominal
interest rate is the annually compounded rate
which would give the same results as the given
rate.- To fi nd the effective rate, fi nd the future value of
$100 for one year at that rate. The effective rate
is the same number as the amount of interest
earned. - Or, as an alternative, Formula 3.3.2 can be used.
Find the equivalent annual
rate for 7.35% compounded
quarterly. (Example 3.3.4)Using Effective Rates for
Comparisons, p. 118- Nominal rates cannot be directly compared if their
compounding frequencies are not the same - To compare nominal rates fairly, compare their
effective rates.
Which rate is highest: 5.95%
compounded annually,
5.85% monthly, or 5.75%
daily? (Example 3.3.7)Using Effective Rates with
“Messy” Terms, p. 120- Effective rates compound annually, so n in the
compound interest formula must be in years. - If the term is not a whole number of years,
decimals and fractions can be used in an
exponent.
Find the future value of a
$20,000 CD for 1000 days at
a 6.25% effective rate.
(Example 3.3.9)Compound Growth Other than
Interest, pp. 121–122- The compound interest formula can be used any
time something is growing at a constant percent
rate, even if the growth is not interest.
A pair of sneakers cost
$75.49 seven years ago. The
price has been rising at a
4.8% growth rate. What is
the price today? (Example
3.3.10)Effective versus Nominal
Rates, p. 129- Calculations done with the effective rate should
match calculations done with the nominal rate - Results will not match exactly because the
effective rate is rounded.
Tris deposited $5,000 at
6.38% compounded daily for
16 years. Find his account’s
future value two ways: using
the nominal rate and by
fi nding the effective rate and
using it. (Example 3.4.3)Solving for Rates and Times
(Optional), pp. 131–132- The compound interest rate can be used to solve
for times and interest rates - The algebra to do this requires the use of
fractional exponents and/or logarithms - The Rule of 72 can provide approximate answers
without requiring as much algebra
How long will it take for
$100 to grow to $500 at 6%
compounded quarterly?
(Example 3.5.4)