Determine the better investment: 4% compounded monthly or 4.2% compounded semiannually
A)4.2% compounded semiannually
B)4%, compounded monthly

Question

Quizplus · Accepted Answer

To determine the better investment, we need to calculate the effective annual rate (EAR) for each option. 
For 4% compounded monthly: 
EAR = (1 + 0.04/12)^12 - 1 
EAR ≈ 0.0407 or 4.07%

For 4.2% compounded semiannually: 
EAR = (1 + 0.042/2)^2 - 1 
EAR ≈ 0.0421 or 4.21%

Since the EAR for 4.2% compounded semiannually is higher than the EAR for 4% compounded monthly, the better investment choice is A) 4.2% compounded semiannually. To determine the better investment, we need to look at the effective annual rate (EAR) for each option.

Option A: 4.2% compounded semiannually 
EAR = (1 + r/n)^n - 1
where r = annual interest rate, n = number of compounding periods in a year

EAR = (1 + 0.042/2)^2 - 1
EAR = 0.04281 or 4.281%

Option B: 4% compounded monthly
EAR = (1 + r/n)^n - 1

EAR = (1 + 0.04/12)^12 - 1
EAR = 0.0406 or 4.06%

As we can see, Option A has a higher effective annual rate than Option B. Therefore, the better investment choice is Option A: 4.2% compounded semiannually.

Determine the Better Investment: 4% Compounded Monthly or 4