Question

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?

Answer 1

Answer:

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.