You are offered ​$100 comma 000 today or ​$310 comma 000 in 15 years. Assuming that you can earn 13​% on your​ money, which should you​ choose?

To solve this problem, we need to compare the present value of the $310,000 that you would receive in 15 years with the $100,000 offered today. This comparison is based on the assumption that you can earn 13% annually.

### Step 1: Present Value Formula
The formula to calculate the present value (PV) of a future amount is:

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

Where:
- $ FV $ = Future value, which is $310,000
- $ r $ = Interest rate per period, which is 13% or 0.13
- $ n $ = Number of periods, which is 15 years

### Step 2: Substituting the values
\[
PV = \frac{310{,}000}{(1 + 0.13)^{15}} = \frac{310{,}000}{(1.13)^{15}}
\]

Now, we will calculate the present value.

\[
PV = \frac{310{,}000}{(1.13)^{15}} = \frac{310{,}000}{6.33707} \approx 48{,}925.68
\]

### Step 3: Conclusion
The present value of $310,000 in 15 years, assuming a 13% annual return, is approximately **$48,925.68**. 

Since $100,000 today is significantly more than $48,925.68, you should choose **$100,000 today**.

---

Would you like further details on the calculations or assumptions?

Here are some related questions you might consider:
1. What if the interest rate were lower, say 10%?
2. How does the present value change if the time period increases to 20 years?
3. What happens if the future value were increased to $400,000 instead of $310,000?
4. How would the decision change if compounding was done monthly instead of annually?
5. Can we apply this present value concept to other financial scenarios, like mortgages or loans?

**Tip**: The higher the interest rate and the longer the time period, the lower the present value of future money.

You are offered $100,000 today or $310,000 in 15 years. Assuming that you can earn 13% on your money, which should you choose?

Compare receiving $100,000 today versus $310,000 in 15 years, assuming a 13% annual return. Learn how to use the Present Value formula to make financial decisions and understand the time value of money. Suitable for high school students in Grades 10-12.

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