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Unformatted text preview: ing for compounding that
occurs during the year
occurs
If you want to compare two alternative
If
investments with different compounding
periods you need to compute the EAR and
use that for comparison.
use 18 Interest Rates: Annual Percentage Rate(APR)
This is the annual rate that is quoted by law
By definition APR = period rate times the number
By
of periods per year
of
Consequently, to get the period rate we rearrange
Consequently,
the APR equation:
the
Period rate = APR / number of periods per
year
You should NEVER divide the effective rate by the
You
number of periods per year – it will NOT give you
the period rate
the 19 EAR  Formula
EAR =(1+ APR
m m ) 1 m = # of compounding
periods in a year Remember that the APR is the annual
quoted rate!
What is the EAR if the APR is 12% Compounded
quarterly?
.12 4
(1+ 4 )  EAR =
= .1255
= 12.55% 1 20 Computing APRs from EARs If you have an effective rate, how can you
compute the APR? Rearrange the EAR equation
and you get:
and
1
m (1 + EAR)
APR = m  1 What is the APR if the EAR is 12.55% and Interest is
compounded quarterly?
1
4 (1 + .1255)
APR = 4 APR = 12.00%  1 Things to Remember about interest rates 21 You ALWAYS need to make sure that the interest
You
rate and the time period match.
rate
If you are looking at annual periods, you need
an annual rate.
If you are looking at monthly periods, you
need a monthly rate.
If you have an APR based on monthly
If
compounding, you have to use monthly periods
for lump sums, or adjust the interest rate
appropriately if you have payments other than
monthly
monthly Annuities and Perpetuities Defined 22 Annuity – finite series of equal payments that
Annuity
occur at regular intervals
occur
If the first payment occurs at the end of the
period, it is called an ordinary annuity
If the first payment occurs at the beginning of the
period, it is called an annuity due Perpetuity – infinite series of equal payments 23 Perpetuity A Perpetuity is an annuity that makes payments
Perpetuity
forever.
forever. Examples
Nobel Prize Endowment
Scholarship Funds In order to withdraw a constant amount forever,
In
never withdraw the principalonly the accrued
interest.
interest. PV = PP
i 24 Perpetuity Example: Donna struck it rich as a result of her education at
ODU. In order to properly thank the faculty she sets
up an endowment to be used for scholarships.
Annual costs are approximately $5,000/year. If
interest rates are currently 5%, how much must she
give to grant one full scholarship per year forever? PV =
PV = 5,000
.05 PP
i = 100,000...
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 Spring '08
 Staff
 Managerial Accounting

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