Question

Sandy McPherson, a university study, has inherited $90,000. She is looking to save this money and earn interest for exactly four years, after which she will use it as a deposit on her new house. She has researched the interest market and come up two good introductory options to choose from:

1. Sum bank- 2.7% interest for the first year, then 1.15 % for the next three years.
2. Certain bank- 2.1% for the first two years and then 0.4% for the next two years.

Assume that interest is paid monthly and that the returns occur after tax.  Task:

1. Calculate the amount of interest Sandy will have earned under each scenario.
2. Taking into consideration the amount of interest earned over the 4 years, calculate the annual rate of return for each product as a percentage.
3. Explain why your answers in question b better represents an APR or an EAR.

Answer 1

a.

Principal Amount = $90,000

SUM BANK - 2.7% interest for the first year, then 1.15 % for the next three years.

Interest earned = 90,000*1.027*1.0115*1.0115*1.0115 - 90,000 = 5,655.647

CERTAIN BANK - 2.1% for the first two years and then 0.4% for the next two years.

Interest earned = 90,000*1.021*1.021*1.004*1.004 - 90,000 = 4,571.749

b.

CAGR = (Future Value/Present Value)^(1/Years of investment) - 1

CAGR for SUM BANK = (90,000*1.027*1.0115*1.0115*1.0115/90,000)^(1/4) - 1 = 6.284%

CAGR for CERTAIN BANK = (90,000*1.021*1.021*1.004*1.004/90,000)^(1/4) - 1 = 5.08%

c.

The answer in question b represents the compounded annual growth rate or overall annual growth rate which is uniform across the years. Unlike the one given in question where multiple interest rates are there within the year which will not help in comparison as there is a compounding effect that is not additive. So for comaprison an uniformity has to be maintained which is possible by CAGR.