Question

You are offered ​$120,000 today or ​$320,000 in 12 years. Assuming that you can earn 15 percent on your​ money, which should you​ choose? If you are offered ​$320,000 in 12 years and you can earn 15 percent on your​ money, what is the present value of $320,000​? $ ____Round to the nearest​ cent.)

Answer 1

first let us know the present value of $320,000 in 12 years.

this can be known using the following formula

=> future amount / (1+r)^n

here,

future amount = $320,000

r = 15%=>0.15.

n=12.

present value of $320,000 in 12 years =>$320,000/ (1.15)^12.

=>$59,810.29.

Amount offer today is $120,000.

Since the amount offered today is greater than the present value of $320,000 received after 12 years, we should choose $120,000 today.

Answer 2

SOLUTION :

It requires to compare the present values of options to select the better one. Higher the PV, better is the option. 

Accordingly, we determine PVs of the two options .

Option 1 :

$120000 today .

Its PV = $120000 .

Option 2 :

Receiving $320000 in 12 years from now. 

Required rate, r = 15% = 0.15

=> 1 + r = 1.15

PV of Option 2 

= FV/(1 + r)^n 

= 320000 / 1.15^12 

= 59810.29 ($) 

PV of Option 2 is = $59810.29 (ANSWER)

So, PV of Option 1 is higher than that of Option 2. 

Hence, Option 1 should be accepted. (ANSWER).