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for
Money chimp assumes annuity due!!!
Payment = $313,497.81 38 Table 6.2 39 Effective Annual Rate (EAR) This is the actual rate paid (or received) after
This
accounting for compounding that occurs during
the year
the
If you want to compare two alternative
If
investments with different compounding periods
you need to compute the EAR and use that for
comparison.
comparison. 40 Annual Percentage Rate This is the annual rate that is quoted by law
By definition APR = period rate times the number of
By
periods per year
periods
Consequently, to get the period rate we rearrange the
Consequently,
APR equation:
APR 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
period 41 Computing APRs What is the APR if the monthly rate is .5%? What is the APR if the semiannual rate is .5%? .5(12) = 6%
.5(2) = 1% What is the monthly rate if the APR is 12% with
What
monthly compounding?
monthly 12 / 12 = 1% 42 Things to Remember You ALWAYS need to make sure that the interest rate
You
and the time period match.
and If you are looking at annual periods, you need an annual
If
rate.
rate.
If you are looking at monthly periods, you need a monthly
If
rate.
rate. If you have an APR based on monthly compounding,
If
you have to use monthly periods for lump sums, or
adjust the interest rate appropriately if you have
payments other than monthly
payments 43 Computing EARs - Example Suppose you can earn 1% per month on $1 invested
Suppose
today.
today. What is the APR? 1(12) = 12%
How much are you effectively earning?
• FV = 1(1.01)12 = 1.1268
• Rate = (1.1268 – 1) / 1 = .1268 = 12.68% Suppose if you put it in another account, you earn 3%
Suppose
per quarter.
per What is the APR? 3(4) = 12%
How much are you effectively earning?
• FV = 1(1.03)4 = 1.1255
• Rate = (1.1255 – 1) / 1 = .1255 = 12.55% 44 EAR - Formula
m APR EAR = 1 +
−1 m Remember that the APR is the quoted rate
m is the number of compounding periods per year 45 Decisions, Decisions II You are looking at two savings accounts. One pays
You
5.25%, with daily compounding. The other pays 5.3%
with semiannual compounding. Which account should
you use?
you First account:
• EAR = (1 + .0525/365)365 – 1 = 5.39% Second account:
• EAR = (1 + .053/2)2 – 1 = 5.37% Which account should you choose and why? 46 Decisions, Decisions II
Decisions,
Continued
Continued Let’s verify the choice. Suppose you invest
Let’s
$100 in each account. How much will you have
in each account in one year?
in First Account:
• Daily rate = .0525 / 365 = .00014383562
• FV = 100(1.00014383562)365 = 105.39 Second Account:
• Semiannual rate = .0539 / 2 = .0265
• FV = 100(1.0265)2 = 105.37 You have more money in the first account. 47 Computing APRs from EARs
Computing If you have an effective rate, how can you
If compute the APR? Rearrange the EAR
equation and you get:
equation (1 + EAR)
APR = m 48 1 m -1 APR - Ex...

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