Answer: 3.1172% Compounded Monthly
Explanation:
[tex] Effective rate of return = ( 1 + r/n)^n - 1 [/tex]
Option A: 3.1196% compounded semiannually.
where r = 3.1196% or 0.031196
n = 2
[tex] Effective Rate of return = (1 + 0.031196/2)^2 - 1 [/tex]
OPTION A : Effective Rate of return = 3.144%
OPTION B: 3.1172% Compounded Monthly
where r = 3.1172% or 0.031172
n = 12
[tex] Effective Rate of return = (1 + 0.031172/12)^12 - 1 [/tex]
OPTION B: Effective Rate of return = 3.162%
OPTION C: 3.1095% Compounded Daily
where r = 3.1095% or 0.031095
n = 365
[tex] Effective Rate of return = (1 + 0.031172/365)^365 - 1 [/tex]
OPTION C :Effective Rate of return = 3.158%
OPTION D: 3.1184% Compounded Quarterly
where r = 3.1184% or 0.031184
n = 4
[tex] Effective Rate of return = (1 + 0.031184/4)^4 - 1 [/tex]
OPTION D :Effective Rate of return = 3.155%
Therefore, OPTION B provides 3.162% the highest APY as compared to the other options.
