Question

9.

Rank the following in order from best (highest rate of return) to worst (lowest rate of return).

Investment One: 12% p.a. compounding continuously

Investment Two: 11% p.a. compounding continuously

Investment Three: 11.50% p.a. compounding semi-annually

Investment Four: 13% p.a. compounding annually

Investment Five: 12% p.a. compounding monthly

Select one:

a. The rank from highest to lowest is: 4, 1, 3, 5, 2

b. The rank from highest to lowest is: 5, 1, 4, 3, 2

c. The rank from highest to lowest is: 1, 2, 5, 3, 4

d. The rank from highest to lowest is: 4, 1, 5, 3, 2.

e. The rank from highest to lowest is: 2, 3, 5, 1, 4

Answer 1

Investment 1:

Effective annual rate = e^r - 1= e^12% - 1 = 1.12749685 - 1 = 0.12749685 = 12.75%

Investment 2:

Effective annual rate = e^r - 1= e^11% - 1 = 1.11627807 - 1 = 0.11627807 = 11.63%

Investment 3:

r = Semi annual interest rate = 11.5% /2 = 5.75%

n = 2 semi annuals

Effective annual rate = (1+r)^n - 1 = (1+5.75%)^2 - 1 = 1.11830625 - 1 = 0.11830625 = 11.83%

Investment 4:

Effective Interest rate is 13%

Investment 5:

r = Semi annual interest rate = 11.5% /2 = 5.75%

n = 2 semi annuals

Effective annual rate = (1+r)^n - 1 = (1+5.75%)^2 - 1 = 1.11830625 - 1 = 0.11830625 = 11.83%

Effective rate for Investment 1 = 12.75%

Effective rate for Investment 2 = 11.63%

Effective rate for Investment 3 = 11.83%

Effective rate for Investment 4 = 13%

Effective rate for Investment 5 = 11.83%

Ranking of Project's from highest to lowest - 4,1,5,3,2

Option d is correct

The rank from highest to lowest is: 4, 1, 5, 3, 2