Question

To find effective interest, there are multiple equations. The most confusing is the difference between equations (1 + i/M) ^ M - 1 and (1 + i/ck) ^c - 1. In what situation would you use each equation, as they give different values.

Answer 1

(1 + i/M) ^ M - 1

This equation is used when nominal interest rate for an year is given and we are supposed to find effective annual yield with m periods of compounding
For example we are given an annual interest rate of 12% and we are supposed to find effective interest rate with quarterly compounding (m=4). In this case, effective annual yield = (1+0.12/4)⁴ -1 = 0.1255 or 12.55%

(1 + i/ck) ^c - 1

This equation is used when we are given returns over a period of k years and we ned to find the annual effective rate with c periods of compounding.
For example if the rate of return for 4 years is 24%, the effective annual return with semiannual compounding (c = 2) is (1+0.24/2*4)⁴ - 1 = 0.0609 or 6.09%