Question

Which do you​ prefer: a bank account that pays 4.8% per year​ (EAR) for three years or

a. An account that pays 2.6% every six months for three​ years?                   

b. An account that pays 7.4% every 18 months for three​ years?                   

c. An account that pays 0.41% per month for three​ years?

​(Note: Compare your current bank EAR with each of the three alternative accounts. Be careful not to round any intermediate steps less than six decimal​ places.)   

Answer 1

Effective Interest rate = [(1+ Interest rate per period)^Number of Compounding] -1

Interest rate per period = Annual interest rate / Number of Compounidng

A) An account that pays 2.6% every six months for three​ years

= [(1+2.6%)^2]-1

= [(1.026)^2]-1

=1.052676 -1

= 0.052676

In Percentage, 0.052676*100

effective annual rate= 5.2676%

B) An account that pays 7.4% every 18 months for three​ years

= [(1+7.4%)^(12/18)] -1

= [(1.074)^(12/18)]-1

= 1.0487440766 -1

= 0.0487440766

In Percentage, 0.0487440766

effective annual rate= 4.8744%

C)An account that pays 0.41% per month for three​ years

= [(1+0.41%)^12]-1

= 1.05032476342 -1

= 0.05032476342

In Percentage, 0.05032476342 * 100

Effective annual rate = 5.032476342%

The Option A has highest effective annual rate, so it should be preferred.