This problem involves calculating the present value (PV) of a growing annuity because you are receiving a series of payments that increase by a constant percentage each year.

Key Information:

• First payment (at the end of year 1): $P_1 = 3600$
• Growth rate of payments: $g = 4\% = 0.04$
• Interest rate (discount rate): $r = 8\% = 0.08$
• Number of payments: $N = 25$

Present Value of a Growing Annuity Formula:

The present value of a growing annuity is given by the formula:

$PV = P_1 \times \left( \frac{1 - \left(\frac{1+g}{1+r}\right)^N}{r - g} \right)$

Where:

• $P_1$ is the first payment.
• $r$ is the discount rate.
• $g$ is the growth rate.
• $N$ is the number of payments.

Substituting Values:

We can now substitute the given values into the formula:

$PV = 3600 \times \left( \frac{1 - \left(\frac{1+0.04}{1+0.08}\right)^{25}}{0.08 - 0.04} \right)$

Let me calculate this value for you.The present value of your aunt's promise, taking into account the 4% annual growth in payments and the 8% discount rate over 25 years, is approximately $54,966.61.

Would you like more details or have any questions about this?

Here are 5 related questions to expand your understanding:

1. How would the present value change if the growth rate were higher?
2. What happens to the present value if the interest rate drops to 6%?
3. How does the present value differ if the first payment is made today instead of a year from now?
4. What if the payments were made indefinitely (i.e., a perpetuity instead of a 25-year annuity)?
5. How does the number of payments affect the present value?

Tip: Always compare the growth rate to the interest rate when calculating the present value of a growing annuity to determine whether the annuity's value will increase or decrease.