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.)
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.
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).
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