Determine the effective annual yield for each investment The

Determine the effective annual yield for each investment. Then select the better investment. Assume 360 days in a year.

14% compounded monthly. Please, explain clearly.

Solution

The formula for compound interest is F = P ( 1 + r)ⁿ where P is the principal, F is the future value r is the rate of interest in decimals for the period and n is the number of periods. Here, let us assume that P = $ 100, and n = 1 year = 12 months. We are given that r = 14 % = (14/100) * (1/12) = 14/1200 . Then, F = 100( 1 + 14/1200)¹² = 100( 1214/1200)¹² = 100 * 1.149342029 = 114.9342029 = $ 114.93 ( on rounding off to the nearest cent). Then the effective yield is ( F - P) /100  = (114.93 - 100)/ 100 = 14.93 % .

NOTE:

The compounding is monthly. Hence n = the number of periods = 12 months. For the same reason, while determining r, we have divided by 12.