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:

 a) Calculate the amount of interest Sandy will have earned under each scenario.

 b) Taking into consideration the amount of interest earned over the 4 years, calculate the annual rate of return for each product as a percentage.

 c) Explain why your answers in question b better represents an APR or an EAR.

Answer 1

a)

PV =90,000

r = 2.7% -1 year 1.15% - next 3 years

n = 4

amount after one year = PV x (1+i)ⁿ

  = 90,000 x(1+0.027/12)¹²

= 92,460.30

amount after 4 years = PV x (1+i)ⁿ

  = 92,460.30 x(1+0.015/12)³⁶

  = 96,713.33

total interest earned over 4 years = 96713.33 - 90000 = 6,713.33

b)

PV =90,000

r = 2.1% -2 year 0.4% - next 2 years

n = 4

amount after one year = PV x (1+i)ⁿ

  = 90,000 x(1+0.021/12)²⁴

= 93,857.06

amount after 4 years = PV x (1+i)ⁿ

  = 93,857.06 x(1+0.004/12)²⁴

  = 94,610.80

interest earned over 4 years = 94610.8 - 90000

= 4,610.8

b) ANNUAL RATE OF RETURN = (ENDING VALUE / BEGINING VALUE )^1/N - 1

CASE 1 = (96713.33 / 90000)^1/4 - 1

=1.01815 - 1

= 1.82%

CASE 2 = (94610.8 / 90000)^1/4 - 1

= 1.01257 -1

= 1.26%

c) IT REPRESENSTS EFFECTIVE ANNUAL RATE(EAR)

The main difference between APR and EAR is that APR is based on simple interest, while EAR takes compound interest into account.HERE IT IS COMPOUNDED ON MONTHLY BASIS THEREFORE IT IS EAR