Activities
Compound
interest - effective rate
Consider three different investments:
-
investment A: 9.0% pa compound interest
payable yearly
-
investment B: 8.8% pa compound interest
payable quarterly
-
investment C: 8.6% pa compound interest
payable monthly
To decide which
is the best investment, consider $1 invested for one year.
The final amounts at the end of the
year are:
-
investment A:
-
investment B:
-
investment C:
Investment B is the best investment
as it provides the highest final amount. It is equivalent to an investment
providing 9.0947% pa compound interest payable yearly. This is called the
effective rate of interest.
The effective
rate of interest is that rate of interest payable yearly which provides
the same final amount. To calculate the effective rate of interest, find
the interest that would be paid on $1 invested for one year.
The effective rates of interest are:
-
investment A: 9.0% pa
-
investment B: 9.0947% pa
-
investment C: 8.9472% pa
Effective rates of interest can also
be calculated on the TI-83 using the:
-
TVM Solver
-
function Eff
(nominal rate, number of interest periods per year).
Nom (effective
rate, number of interest periods per year)
This function calculates the nominal
rate of interest.
The following investments give an
effective rate of interest of 7.5% pa:
-
7.298% pa payable quarterly
-
7.254% pa payable monthly
-
7.233% pa payable daily.
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