EAR = [1 + (APR /
m
)]
m
– 1
EAR = [1 + (.08 / 4)]
4
– 1 = .0824 or 8.24%
EAR = [1 + (.16 / 12)]
12
– 1 = .1723 or 17.23%
EAR = [1 + (.12 / 365)]
365
– 1 = .1275 or 12.75%
To find the EAR with continuous compounding, we use the equation:
EAR = e
q
– 1
EAR = e
.15
– 1 = .1618 or 16.18%
13.
Here we are given the EAR and need to find the APR. Using the equation for discrete
compounding:
EAR = [1 + (APR /
m
)]
m
– 1
We can now solve for the APR. Doing so, we get:
APR =
m
[(1 + EAR)
1/
m
– 1]
EAR = .0860 = [1 + (APR / 2)]
2
– 1 APR = 2[(1.0860)
1/2
– 1] = .0842 or 8.42%
EAR = .1980 = [1 + (APR / 12)]
12
– 1 APR = 12[(1.1980)
1/12
– 1] = .1820 or 18.20%
EAR = .0940 = [1 + (APR / 52)]
52
– 1 APR = 52[(1.0940)
1/52
– 1] = .0899 or 8.99%
Solving the continuous compounding EAR equation:
EAR = e
q
– 1
We get:
APR = ln(1 + EAR)
APR = ln(1 + .1650)
APR = .1527 or 15.27%
14.
For discrete compounding, to find the EAR, we use the equation:
EAR = [1 + (APR /
m
)]
m
– 1
So, for each bank, the EAR is:
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 Spring '08
 spurlin
 Compounding, Debt

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