Homework 8 Solution
1.
A local credit union is advertising a car loan with an APR of 4.5%. If interest is compounded
monthly, what is the equivalent annual interest rate (i.e., APY)?
Since interest is compounded monthly, we should start by dividing the nominal annual rate
by 12 to convert it into a real monthly rate:
4.5% per year
r
i
M
12 months per year
0.375% per month
Now we can compound that monthly rate over 12 months to get the equivalent annual rate:
M1
2
a
i
1 i
1
1.00375
1
0.0459
4.59% per year
We could also convert the APR directly into an APY using the formula in the book:
m1
2
eff
r0
.
0
4
5
i
1
1
1
1
0.0459
4.59% per year
2
2. My credit card charges 0.0425% per day on the outstanding balance. What is the APR for
this credit card? What is the APY? Assume 360 days in a year.
The APR is just the rate per compounding period multiplied by the number of compounding
periods in a year. If we assume there are 360 days in a year, then:
r
0.0425% per day 360 days per year
15.3% per year
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 Fall '08
 Moore,L
 Annual Percentage Rate, Interest, Adams County, Adams County Road Commission

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