Question

Mia is thinking about taking out a home loan. She receives the following offers from 4 banks. Assume all other costs are the same for each bank, which offer should Mia accept?

A. 4.1% p.a. compounded monthly

B. 4.05% p.a. compounded quarterly

C. 2.1% effective per half year

D. 4% p.a. effective

Answer 1

Mia should select offer "D".

 

Explanation:

Mia should accept the offer whose effective annual rate is lower:

 

Calculation of the effective annual rate:

Effective annual rate = (1+ Nominal rate/m)^m - 1

where, m = Number of compounding in a year

 

solve,

 

A. 4.1% p.a. compounded monthly

Effective annual rate = (1+ 0.041/12)^12 - 1

                                  = 1.0418 - 1

                                  = 0.0418 or 4.18% 

 

B. 4.05% p.a. compounded quarterly:

Effective annual rate = (1+ 0.0405/4)^4 - 1

                                  = 1.0411 - 1

                                  = 0.0411 or 4.11%

 

C. 2.1% effective per half year:

Effective annual rate = (1+ 0.021)^2 - 1

                                  = 1.0424 - 1

                                  = 0.0424 or 4.24%

 

D. Effective annual rate = 4% 

 

From the above working, it can be seen that the effective annual rate of the offer D is lower, Mia should select offer "D".

From the above working, it can be seen that the effective annual rate of the offer D is lower, Mia should select offer "D"