Principles of Finance · free preview
Stated versus Effective Rates
The stated annual rate ignores compounding within the year, the effective annual rate includes it, and converting between them with the compounding count lets borrowers compare loans and savers compare deposits honestly.
1. Two ways to quote one loan
Two ways to quote one loan
2. The conversion formula
The conversion formula
3. The Truth in Lending context
The Truth in Lending context
4. Frequency as value
Frequency as value
5. The stated rate's flaw
Why does the stated annual rate understate the true annual cost of a loan with monthly compounding?
6. Converting 12 percent monthly
What is the effective annual rate of 12 percent compounded monthly?
7. Comparing two deposits
Bank A offers 8 percent compounded annually, Bank B offers 7.9 percent compounded daily. Which is the better deposit?
8. The quarterly comparison
Which loan is cheaper at the same 12 percent stated rate, one compounded quarterly or one compounded monthly?
9. The continuous limit
What happens to the effective annual rate as the compounding frequency m grows without bound?
10. Why regulation discloses APR
Why do lending regulations require disclosure of the annual percentage rate?
11. The monthly piece of 12 percent
A stated annual rate of 12 percent compounded monthly corresponds to what monthly rate in percent? Write the number.
12. The exponent's count
In the effective rate formula, what letter names the number of compounding periods per year? Write the letter.
13. The better deposit frequency
At the same stated rate, a saver should prefer which compounding frequency, annual or daily? Answer with one word.
14. The ceiling constant
What mathematical constant, approximately 2.718, appears in the continuous compounding limit of the effective rate formula? Answer with one letter.
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