Question

​(​Present-value comparison​) You are offered $2,000 ​today, ​$6,000 in 14 ​years, or ​$32,000 in 20 years. Assuming that you can earn 7 percent on your​ money, which offer should you​ choose?

a. What is the present value of ​$32,000 in 20 years discounted at 7 percent interest​ rate?

​$ ​ (Round to the nearest​ cent.)

b. What is the present value of ​$6,000 in 14 years discounted at 7 percent interest​ rate?

​$ ​(Round to the nearest​ cent.)

c. Which offer should you​ choose? ​ (Select the best choice​ below.)

A. Choose ​$6,000 in 14 years because its present value is the highest.

B. Choose ​$2,000 today because its present value is the highest.

C. Choose ​$32,000 in 20 years because its present value is the highest.

Answer 1

Present value is the today value or current value of amount to be received in future.
Present value = Future value*(1/(1+r)^n)
where r = interest rate
n = number of years.
a.
Calculation of present value
Present value	32000*(1/(1+0.07)^20)
Present value	32000*(1/(1.07^20))
Present value	32000*0.25842
Present value	$8,269.41
Thus, present value of $32,000 is $8,269.41
b.
Calculation of present value of $6,000 in 14 years.
Present value	6000*(1/(1+0.07)^14)
Present value	6000*(1/(1.07^14))
Present value	6000*0.38782
Present value	$2,326.90
Thus, present value of $6,000 is $2,326.90
c.
The present value in case of $32,000 is the highest among other two options and therefore choose $32,000 in 20 years.
Correct answer is option ( c)