Question

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

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: 2, 3, 5, 1, 4

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

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

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

Solutions

Expert Solution

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

Explanation:

In order to rank the investments according to the returns we need to calculate the Effective Annual Return (EAR) of the investments.
The ranking will be based on the EAR. Higher the EAR higher is the rate of return.

Investment One: 12% P.A... compounding continuously

Formula of EAR in case of continuous compounding
EAR = e^r -1
where r = Interest P.A...

EAR = 2.71828^0.12 -1
EAR = 1.127497 -1
EAR = 0.127497 or 12.75%

Investment Two : 11% P.A... compounding continuously

Formula of EAR in case of continuous compounding
EAR = e^r -1
where r = Interest P.A...

EAR = 2.71828^0.11 -1
EAR = 1.116278 -1
EAR = 0.116278 or 11.63%

Investment Three: 11.50% P.A... compounding semi-annually

Formula of EAR in case of semi-annual compounding
EAR = (1+r/m)^m -1
where r = Interest P.A...
m = number of compounding periods (semiannual compounding means m = 2)

EAR = (1+0.115/2)^2 -1
EAR = (1.0575)^2 -1
EAR = 0.118306 or 11.83%

Investment Four: 13% P.A... compounding annually
For Annual Compounding
EAR = Annual Rate of interest
EAR =13%

Investment Five: 12% P.A... compounding monthly

Formula of EAR in case of monthly compounding
EAR = (1+r/m)^m -1
where r = Interest P.A...
m = number of compounding periods (monthly compounding means m = 12)

EAR = (1+0.12/12)^12 -1
EAR = (1.01)^12 - 1
EAR = 0.126825 or 12.68%

Ranking Table

Investments	EAR	Rank
Investment One: 12% P.A... compounding continuously	12.75%	2
Investment Two: 11% P.A... compounding continuously	11.63%	5
Investment Three: 11.50% P.A... compounding semi-annually	11.83%	4
Investment Four: 13% P.A... compounding annually	13%	1
Investment Five: 12% P.A... compounding monthly	12.68%	3

jeff jeffy answered 1 year ago

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