You are offered ​$100 comma 000 today or ​$310 comma 000 in 14 years. Assuming that you can earn 7​% on your​ money, which should you​ choose?  

This problem involves the concept of present value (PV), which helps determine which option is better by comparing the value of future cash (in this case, $310,000) to the value of money today ($100,000). The formula for present value is:

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

Where:
- $ PV $ = present value
- $ FV $ = future value ($310,000)
- $ r $ = interest rate (7% or 0.07)
- $ t $ = time period (14 years)

Let's calculate the present value of $310,000 in 14 years. 

\[
PV = \frac{310,000}{(1 + 0.07)^{14}}
\]

Now, I'll compute the result.The present value of receiving $310,000 in 14 years, assuming a 7% interest rate, is approximately $120,223.34.

Since the present value of $310,000 in 14 years is higher than the $100,000 offered today, you should choose the $310,000 in 14 years.

Would you like further details or have any questions? 

Here are five related questions you might consider:
1. How does the interest rate affect the decision between present and future values?
2. What if the interest rate were different, say 5% or 10%?
3. How does the time period (14 years) impact the present value calculation?
4. Can you apply the same formula to calculate the future value of the $100,000 today after 14 years?
5. How would inflation affect the comparison between present and future money?

**Tip**: Always compare cash flows using the same point in time (e.g., present value) to make informed financial decisions.

You are offered $100,000 today or $310,000 in 14 years. Assuming that you can earn 7% on your money, which should you choose?

Learn how to use the present value formula to decide whether to take $100,000 today or wait for $310,000 in 14 years, assuming a 7% interest rate. This detailed solution covers key financial concepts such as interest rates, present value, and the time value of money. Suitable for students in Grades 10-12.

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