Question

You are a young personal financial adviser. Molly, one of your clients approached you for consultation about her plan to save aside $450,000 for her child’s higher education in 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 a saving 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: 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 if 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 saving account to get the $450,000 ready in just 10 years from now? d) Calculate the monthly payment Molly needs to contribute into ANZ Investment Fund to get $330,000 after 15 years in Investment 2? 3 e) In investment 2, if Molly changes to contribute $1200/month to that super fund at the beginning of each month, how much money she would have in ANZ Investment fund after 15 years? f) Molly is offered an investment that will pay $12 000 each year forever. How much should she pay for this investment if the rate of return 12% applies? (1 mark)

Answer 1

Part (a):

EAR= (1+R/t)^t-1

Where

R= interest rate per year and t= number of times compounded a year

Bank A:

R= 8.5%, t= 2

EAR= (1+0.085/2)^2-1= 8.680625%

Bank B:

R= 8.45%, t=4

EAR=(+0.0845/4)^4-1 = 8.721550%

Molly should choose Bank B, based on the EAR.

Part (b):

Money accumulated in 15 years by choosing Bank B= P(1+R/t)^nt

Where P= Principal ($120,000), n=period (15 years)

Money accumulated in 15 years= 120,000*(1+8.45%/4)^(15*4) = $420,645.06

Part (c):

Rate of interest compounded annually R= (F/P)^(1/n)-1

Where F= Future value, P= Principal and n= Period (number of years)

Given, F= $450,000    P= $120,000   and n= 10 years

Rate of interest= (450000/120000)^(1/10)-1 = 14.13087%

Part (d):

Amount to be invested at the end of each month for 15 years= $1,041.13 as follows:

Part (e):

Money available after 15 years if paid $1200 per month, at the beginning of each month= $382,573.49

Calculation as follows:

Part (f):

Payment of $12,000 a year forever constitutes a perpetuity. Amount to be paid now is the present value (PV) of the perpetuity.

PV of perpetuity= C/r

Where C= periodical payment ($12,000) and r= interest rate (12%)

Amount to be paid now= 12000/0.12= $100,000