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Part 1

​(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 comma 2001,200 

​today, 

​$5 comma 0005,000 

in 

1515 

​years, or 

​$33 comma 00033,000 

in 

3030 

years.  Assuming that you can earn 

77 

percent on your​ money, which should you​ choose?

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Part 1

If you are offered 

​$5 comma 0005,000 

in 

1515 

years and you can earn 

77 

percent on your​ money, what is the present value of 

​$5 comma 0005,000​?

​$1,812.231,812.23  

​(Round to the nearest​ cent.)

Part 2

If you are offered 

​$33 comma 00033,000 

in 

3030 

years and you can earn 

77 

percent on your​ money, what is the present value of 

​$33 comma 00033,000​? 
 
​$enter your response here  

​(Round to the nearest​ cent.)

To determine which option is best, we need to compare the present value of the different payment options. The present value (PV) is calculated using the formula:

\[
PV = \frac{FV}{(1 + r)^n}
\]

Where:
- $PV$ is the present value.
- $FV$ is the future value (amount received in the future).
- $r$ is the interest rate (7% = 0.07 in decimal form).
- $n$ is the number of years until the payment is received.

### Part 1:
For the second option: $5,000 in 15 years, we calculate the present value.

\[
PV = \frac{5,000}{(1 + 0.07)^{15}}
\]

Let me calculate this value.The present value of receiving \$5,000 in 15 years, assuming a 7% annual return, is approximately **\$1,812.23**.

### Part 2:
Now, for the third option: \$33,000 in 30 years, we calculate the present value using the same formula.

\[
PV = \frac{33,000}{(1 + 0.07)^{30}}
\]

Let me calculate this now.The present value of receiving \$33,000 in 30 years, assuming a 7% annual return, is approximately **\$4,335.11**.

### Comparison:
- \$1,200 today has a present value of \$1,200.
- \$5,000 in 15 years has a present value of \$1,812.23.
- \$33,000 in 30 years has a present value of \$4,335.11.

Since the present value of \$33,000 in 30 years is the highest, it is the best option to choose.

Would you like further details or clarifications? Here are 5 related questions to consider:

1. How does the interest rate affect the present value in long-term investments?
2. What would be the present value of \$10,000 received in 20 years at 7% interest?
3. How does inflation impact decisions involving future payments?
4. What is the relationship between time and the discount factor in present value calculations?
5. How would different compounding frequencies (e.g., monthly vs. yearly) impact the present value?

**Tip**: Always compare the present value when evaluating different payment options received at different times.

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: $1,200 today, $5,000 in 15 years, or $33,000 in 30 years. Assuming that you can earn 7% on your money, which should you choose?

Part 1: If you are offered $5,000 in 15 years and can earn 7% on your money, what is the present value of $5,000?

Part 2: If you are offered $33,000 in 30 years and can earn 7% on your money, what is the present value of $33,000?

Learn how to calculate the present value of $5,000 received in 15 years and $33,000 received in 30 years at an interest rate of 7%. This solution demonstrates the time value of money using the present value formula. Suitable for advanced high school or college-level students.

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