Question

An investor has a choice of investing a sum of money at 7.5% compounded annually or 7.4% compounded semiannually or 7.2% compounded quarterly. Which alternative is the best one for the investor?

Answer 1

Calculating the Effective Annual Rate(EAR) of each choices:-

i). 7.5% compounded annually

Where,

r = Interest rate = 7.5%

m = no of times compounding in a year = 1 (compounded annually)

EAR = 1.075 - 1

EAR = 7.5%

ii). 7.4% compounded semiannually

Where,

r = Interest rate = 7.4%

m = no of times compounding in a year = 2 (compounded semiannually)

EAR = 1.075369 - 1

EAR = 7.5369%

iii). 7.2% compounded quarterly

Where,

r = Interest rate = 7.2%

m = no of times compounding in a year = 4 (compounded quarterly)

EAR = 1.073967 - 1

EAR = 7.3967%

So, 7.4% compounded semiannually is the best alternative.