Lenny Loanshark charges “1 point” per week (that is, 1% per week) on his
loans. What APR must he report to consumers? Assume exactly 52 weeks in
a year. What is the effective annual rate?
Explanation
Some values below may show as rounded for display purposes, though unrounded numbers should be used for actual calculations.
| APR |
= |
Rate per period × Number of periods per year |
| |
= |
1.10% × 52 |
| |
= |
57.20% |
| APR |
= |
(1 + Rate per period) Number of periods per year – 1 |
| |
= |
1.011052 – 1 |
| |
= |
.7663, or 76.63% |
You can also calculate the EAR as:
| EAR |
= |
[1 + APR / t]t – 1 |
| |
= |
[1 + (.5720 / 52)]52 – 1 |
| |
= |
.7663, or 76.63% |
Your calculator may also have an ICONV function.
Calculator computations:
| NOM |
= |
APR |
| C/Y |
= |
52 |
| EFF |
= |
Effective Annual Rate |
| NOM |
= |
57.20 |
| C/Y |
= |
52 |
| CPT EFF |
= |
76.63 |
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