Question

Consider the following​ alternatives: i. $130 received in one year ii. $230 received in five years iii. $ 350 received in 10 years a. Rank the alternatives from most valuable to least valuable if the interest rate is 9 % per year. b. What is your ranking if the interest rate is 3 % per​ year? c. What is your ranking if the interest rate is 13 % per​ year?

Rank the alternatives from most valuable to least valuable if the interest rate is 9 %per year.

First calculate the present value​ (PV) of each​ alternative:

The PV of $130 received in one year if the interest rate is 9 % per year is? ​(Round to the nearest​ cent.)

The PV of $ 230 received in 5 years if the interest rate is 9 % per year is​(Round to the nearest​ cent.)

The PV of $ 350 received in 10 years if the interest rate is 9%per year is (Round to the nearest​ cent.)

Next, rank the choices by their​ PV:  ​(Select the best choice​ below.)

A.The ranking of the projects​ is:option i​>option iii​>option ii

B.The ranking of the projects​ is:option ii​>option i​>option iii

C.The ranking of the projects​ is: option ii >option iii >option i.

D.The ranking of the projects​ is:option iii ​>option ii >option i

part B

b. What is your ranking if the interest rate is only 3% per​ year?

First calculate the present value​ (PV) of each​ alternative:

The PV of $130 received in 1 year if the interest rate is 3% per year is (Round to the nearest​ cent.)

The PV of $230 received in 5 years if the interest rate is 3 %per year is​(Round to the nearest​ cent.)

The PV of $350 received in 10years if the interest rate is 3 % per year is ?​(Round to the nearest​ cent.)

Next rank the choices by their​ PV:  ​(Select the best choice​ below.)

A.The ranking of the projects​ is:option ii>option iii​>option i

B.The ranking of the projects​ is:option i>option ii​>option iii

C.The ranking of the projects​ is:option iii​>option ii​>option i

D.The ranking of the projects​ is:option iii>option i​>option ii

Part C

What is your ranking if the interest rate is

13 %13%

per​ year?

First calculate the present value​ (PV) of each​ alternative:

The PV of $ 130 received in one year if the interest rate is 13 % per year is (Round to the nearest​ cent.)

The PV of $ 230 received in 5 years if the interest rate is13 %per year is ​(Round to the nearest​ cent.)

The PV of $ 350 received in 10years if the interest rate is 13 % per year is ​(Round to the nearest​ cent.)

Next rank the choices by their​ PV: ​(Select the best choice​ below.)

A.The ranking of the projects​ is:option iii>option i​>option ii

B.The ranking of the projects​ is: option ii​>option i>option iii

C.The ranking of the projects​ is: option ii​>option iii​>option i.

D.The ranking of the projects​ is: option i>option option ii>option iii

Answer 1

Present value = Future value/(1+i)^n

i = interest rate per period

n= number of periods

a)

Rate = 9%

i) PV = 130/1.09 = 119.27

ii) PV = 230/1.09^5 = 149.48

iii) PV = 350/1.09^10 = 147.84

C.The ranking of the projects​ is: option ii >option iii >option i.

b)

Rate = 3%

i) PV = 130/1.03 = 126.21

ii) PV = 230/1.03^5 = 198.40

iii) PV = 350/1.03^10 = 260.43

C.The ranking of the projects​ is:option iii​>option ii​>option i

c)

Rate = 13%

i) PV = 130/1.13 = 115.04

ii) PV = 230/1.13^5 = 124.84

iii) PV = 350/1.13^10 = 103.11

B.The ranking of the projects​ is: option ii​>option i>option iii