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.

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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.