Question

Which of the following offers the highest return?

        A. 12% nominal rate compounded monthly

        B. 12.4% nominal rate compounded quarterly

        C. 12.8% nominal rate compounded semi-annually

        D. 13.0% nominal rate compounded annually

        E. More information is needed to determine the best investment.

Answer 1

Option A:

Annual Interest Rate, APR = 12%
Compounding Period per year, n = 12

Effective Annual Rate, EAR = (1 + APR/n)^n - 1
Effective Annual Rate, EAR = (1 + 0.12/12)^12 - 1
Effective Annual Rate, EAR = 1.01^12 - 1
Effective Annual Rate, EAR = 1.1268 - 1
Effective Annual Rate, EAR = 0.1268 or 12.68%

Option B:

Annual Interest Rate, APR = 12.4%
Compounding Period per year, n = 4

Effective Annual Rate, EAR = (1 + APR/n)^n - 1
Effective Annual Rate, EAR = (1 + 0.124/4)^4 - 1
Effective Annual Rate, EAR = 1.031^4 - 1
Effective Annual Rate, EAR = 1.1299 - 1
Effective Annual Rate, EAR = 0.1299 or 12.99%

Option C:

Annual Interest Rate, APR = 12.8%
Compounding Period per year, n = 2

Effective Annual Rate, EAR = (1 + APR/n)^n - 1
Effective Annual Rate, EAR = (1 + 0.128/2)^2 - 1
Effective Annual Rate, EAR = 1.064^2 - 1
Effective Annual Rate, EAR = 1.1321 - 1
Effective Annual Rate, EAR = 0.1321 or 13.21%

Option D:

Annual Interest Rate, APR = 13.00%
Compounding Period per year, n = 1

Effective Annual Rate, EAR = (1 + APR/n)^n - 1
Effective Annual Rate, EAR = (1 + 0.13/1)^1 - 1
Effective Annual Rate, EAR = 1.13^1 - 1
Effective Annual Rate, EAR = 1.13 - 1
Effective Annual Rate, EAR = 0.13 or 13.00%

So, Option C offers the highest return.