A rich aunt has promised you $3,600.00, one year from today. In addition, each year after that , she has promised a payment (on the anniversary of the last payment) that is 4.00% larger than the last payment. She will continue to show this generosity for 25 years, giving a total of 25 payments. If the interest rate is 8.00%, what is her promise worth today?

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.

A rich aunt has promised you $3,600.00, one year from today. In addition, each year after that, she has promised a payment (on the anniversary of the last payment) that is 4.00% larger than the last payment. She will continue to show this generosity for 25 years, giving a total of 25 payments. If the interest rate is 8.00%, what is her promise worth today?

Calculate the present value of a 25-year growing annuity, where the first payment of $3,600 increases by 4% annually. Learn how the interest rate of 8% affects the valuation of future payments using the Present Value of a Growing Annuity formula. Suitable for finance students and advanced high school learners.

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