Question

You are a young personal financial adviser. Molly, one of your clients approached you for a consultation about her plan to save aside $450,000 for her child’s higher education in the United States 15 years from now. Molly has a saving of $120,000 and is considering different alternative options:

Investment 1: Investing that $120,000 in savings account for 15 years. There are two banks for her choice. Bank A pays a rate of return of 8.5% annually, compounding semi-annually. Bank B pays a rate of return of 8.45 annually, compounding quarterly.

Investment 2: Putting exactly an equal amount of money into ANZ Investment Fund at the end of each month for 15 years to get 330 000 she still shorts of now. The fund is offering a rate of return 7% per year, compounding monthly.

Required: Work on the question a, b, and c only

a) Identify which Bank should Molly choose in Investment 1 by computing the effective annual interest rate (EAR)?

b) Calculate the amount of money Molly would accumulate in Investment 1 after 15 years is she chooses Bank B?

c) How much is the annual interest rate, assuming compounding annually Molly should aim at if she chooses to invest her $120 000 in a savings account to get the 450,000 funds ready in just 10 years from now?

Answer 1

a.) Bank to choose for Investment 1

Bank A

Annual Rate - 8.5%

Compounding - Semi-annualy

EAR (I) Formual

i=(1+r/m)^m−1

=(1+0.0852/)^2−1

i=(1+0.0852)^2−1

i=0.086806

I=i×100=8.68%

Bank B

Annual Rate - 8.45%

Compounding - Quaretrly

i=(1+0.0845/4)^4−1

i=(1+0.0845/4)^4−1

i=0.087216

I=i×100=8.72%

She should invest in Bank B which pays a higher interest rate.

b.) Amount accumulated in Bank B

Where: A = P(1 + r/n)^nt

A = 120,000(1+8.45%/4)^4*15

A = $ 420,645.06

A = P + I where
P (principal) = $ 120,000.00
I (interest) = $ 300,645.06