An annuity provides for 12 annual payments. The first payment is $100, paid at the end of the first year, and each subsequent payment is 5.0% more than the one preceding it. Calculate the present value of this annuity if i=0.07.

This problem involves calculating the **present value (PV)** of a growing annuity. The payments increase by a constant percentage each year, and the first payment starts at $100.

The formula for the present value of a growing annuity is:

\[
PV = P_1 \times \frac{1 - \left(\frac{1+g}{1+i}\right)^n}{i - g}
\]

Where:
- $ P_1 $ is the first payment (\$100),
- $ g $ is the growth rate of the payments (5.0% or 0.05),
- $ i $ is the discount rate (7.0% or 0.07),
- $ n $ is the number of payments (12).

Let's calculate the present value using this formula.

\[
PV = 100 \times \frac{1 - \left(\frac{1+0.05}{1+0.07}\right)^{12}}{0.07 - 0.05}
\]

I'll compute this now.The present value of the annuity is approximately **$1,013.09**.

Would you like a detailed explanation of how this was computed, or do you have any specific questions?

Here are 5 related questions that might interest you:
1. How does the formula for the present value of an annuity differ if the payments are constant?
2. How would the present value change if the interest rate were different?
3. What would happen to the present value if the growth rate were negative?
4. How do you calculate the future value of a growing annuity?
5. What is the difference between an ordinary annuity and an annuity due?

**Tip:** When calculating the present value of an annuity with growing payments, be careful to distinguish between the growth rate and the interest rate. They both influence the value, but in opposite directions!

Learn how to calculate the present value of a growing annuity with 12 annual payments. The first payment is $100, increasing by 5% annually, with a discount rate of 7%. This detailed solution uses the present value formula for a growing annuity, suitable for students in Grades 11-12.

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