10.10: A Word on Compounding Frequency and Annual Equivalent Rates
Questions:
- What is the difference between 10% annual rate, compounded annually versus a 10% annual rate, compounded quarter- in terms of FV of $1?
- How may the two rates be equated? In other words, how may I define the annual frequency at a rate equivalent to the quarterly frequency?
- What happens as the compounding frequency increases?
Solution to Question #2 :
In general, (1 + R/ p ) np = FV
Annually, (1.10) 1 = 1.10
versus
Quarterly, (1 + .10/4) 1 x 4 = (1.025) 4 = 1.1038
That is, 10% quarterly is equivalent to 10.38% annually!
In other words, the Annual Percentage Rate ( APR ) for 10% compounded quarterly, is 10.38%!