In the continuous compounding equation, the interest rate is the stated or nominal annual rate.
Example:Given: a 10% annual rate paid quarterly; PV = 500; time is 5 years; compute FV.
Solve: I = 10/4 = 2.5; N = 5 * 4 = 20; PV = 500: compute FV = 819.31.
i: Distinguish between the stated annual interest rate and the effective annual rate.
The stated rate of interest is known as the nominal rate, and represents the contractual rate. The periodic rate, in contrast, is the rate of interest earned over a single compound period - e.g., a stated (nominal) rate of 12%, compounded quarterly, is equivalent to a periodic rate of 12/4 = 3%. Finally, the true rate of interest is known as the effective rate and represents the rate of return actually being earned, after adjustments have been made for different compounding periods.
j: Calculate the effective annual rate, given the stated annual interest rate and the frequency of compounding.
Example:Compute the effective rate of 12%, compounded quarterly. Given m = 4, and periodic rate = 12/4 = 3%.
Effective rate = (1 + periodic rate)m- 1
Where m = the number of compounding periods in a year.
(1 + .03)