Question

4. You have $100 and think where to invest your money. You have three options. Option A promises you a weekly interest rate of 0.3%, compounded weekly. Option B promises a 16% annual interest rate with one payment at the end of each year. Finally, option C has a quoted annual rate of 15% with quarterly compounding. Assume that a year consists of 52 weeks.

   (a) (3 points) What are APRs of the three investment opportunities? (b) (6 points) Rank these investment opportunities by their attractiveness to you. (c) (6 points) How much more will earn over 10 years if you invest in your most preferable option relative to your least preferable option?

Answer 1

Effective Interest Rate or EAR = [{1+(APR/n)}^n]-1

Where, APR = Annual Interest Rate or Nominal Rate, n = Number of times compounded in a year

Option A:

APR = Weekly Interest Rate*52 = 0.3%*52 = 15.6%

EAR = [{1+(0.156/52)}^52]-1 = 0.16855= 16.855%

Option B:

APR = EAR = 16%

Option C:

APR = Quoted Annual Rate = 15%

EAR = [{1+(0.15/4)}^4]-1 = 0.15865 = 15.865%

Higher the EAR, Better the Investment. Accordingly,

Rank 1: Option A

Rank 2: Option B

Rank 3: Option C

Future Value after 10 years = Present Value*[(1+EAR)^10]

Option A = 100*[(1+0.16855)^10] = 100*4.74758 = $474.76

Option C = 100*[(1+0.15865)^10] = 100*4.36037 = $436.04

Amount Earned MORE = 474.76-436.04 = $38.72