(Present value comparison) Much to your surprise, you were selected to appear on

Question

(Present value comparison) Much to your surprise, you were selected to appear on the TV show "The Price is Right". As a result of your prowess in identifying how many rolls of toilet paper a typical American family keeps on hand, you win the opportunity to choose one of the following: $1,900 today, $7,000 in 10 years, or $25,000 in 29 years. Assuming that you can earn 16 percent on your money, which should you choose?

(A) If you are offered $7,000 in 10 years and you can ear 11% on your money, what is the present value of $7,000?

(B) If you are offered $25,000 in 29 years and you can earn 11 percent on your money, what is the present value of $25,000?

(C) Which offer should you choose?

Explanation / Answer

When the Interest Rate is 16%

Part A)

The present value of a lumpsum payment can be calculated with the use of following formula:

Present Value = Lumpsum Amount/(1+Rate)^n where n = Years

__________

Using the information provided in the question, we get,

Present Value = 7,000/(1+16%)^10 = $1,586.79

__________

Part B)

The present value of a lumpsum payment can be calculated with the use of following formula:

Present Value = Lumpsum Amount/(1+Rate)^n where n = Years

__________

Using the information provided in the question, we get,

Present Value = 25,000/(1+16%)^29 = $337.80

__________

Part C)

Option A (1,900 today) should be chosen as it provides the highest Present Value.

_______________________

When the Interest Rate is 11%

Part A)

The present value of a lumpsum payment can be calculated with the use of following formula:

Present Value = Lumpsum Amount/(1+Rate)^n where n = Years

__________

Using the information provided in the question, we get,

Present Value = 7,000/(1+11%)^10 = $2,465.29

__________

Part B)

The present value of a lumpsum payment can be calculated with the use of following formula:

Present Value = Lumpsum Amount/(1+Rate)^n where n = Years

__________

Using the information provided in the question, we get,

Present Value = 25,000/(1+11%)^29 = $1,212.20

__________

Part C)

Option B ($7,000 in 10 Years) should be chosen as it provides the highest Present Value.

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