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**Unformatted text preview: **her than monthly
payments 41
41 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%
42
42 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 43
43 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? 44
44 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. 45
45 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 1 m -1 46
46 APR - Example Suppose you want to earn an effective rate of
Suppose
12% and you are looking at an account that
compounds on a monthly basis. What APR must
they pay?
they [ APR = 12 (1 + .12)
or 11.39% 1 / 12 − 1 = .1138655152 47
47 Computing Payments with
Computing
APRs
APRs Suppose you want to buy a new computer system and
Suppose
the store is willing to sell it to allow you to make
monthly payments. The entire computer system costs
$...

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