Which do you prefer: a bank account that pays 5 %5% per year (EAR) for three years or: a. An account that pays 2.5 %2.5% every six months for three years? b. An account that pays 7.5 %7.5% every 18 months for three years? c. An account that pays 0.5 %0.5% per month for three years?

c. An account that pays 0.5 %0.5% per month for three years.

Explanation:

We can evaluate all the option using following formula:

EAR = (1 + (r / m)) ^m - 1

a.

2.5% every six months for three years

r = 2.5% = 0.025 / 6 =

m = 12/6 = 2

EAR = (1 + 0.025) ^2 - 1

EAR = 0.050625 = 5.06%

7.5% every 18 months for three years

r = 7.5% for 1.5 years = 7.5% / 18 = 0.4167% per month = 0.004167 per month

EAR = (1 + 0.004167) ^12 - 1

EAR = 0.051166 = 5.12%

0.5% every month for three years

r = 0.5% = 0.005

EAR = (1 + 0.005) ^12 - 1

EAR = 0.0616778 = 6.17%

We will prefer an account that pays 0.5 %0.5% per month for three years, it pays the highest return.