Melinda has recently purchased a house and expects that the roof will need replacement 
in 20 years, which will cost approximately $25,000. To ensure she has the necessary 
funds for this future expense, she plans to save an equal sum of money at the end of 
each year. Her savings will be invested and will accrue a 6% annual interest rate. What 
is the amount she should set aside annually for this purpose, and should you calculate 
the future value or present value or annuity?


To solve this problem, we need to calculate the **annual payment (PMT)** Melinda should set aside to reach her goal of $25,000 in 20 years, assuming the interest rate is 6% annually. Since the future value is known ($25,000), this is a **future value of an ordinary annuity** problem.

### Step-by-step breakdown:

1. **Future Value of Annuity Formula:**
   \[
   FV = PMT \times \frac{(1 + r)^n - 1}{r}
   \]
   where:
   - $ FV $ = Future Value = $25,000
   - $ PMT $ = Annual payment (the amount we are solving for)
   - $ r $ = Interest rate per period (6% or 0.06)
   - $ n $ = Number of periods (20 years)

2. **Rearrange the formula to solve for PMT:**
   \[
   PMT = \frac{FV \times r}{(1 + r)^n - 1}
   \]

3. **Substitute the known values:**
   \[
   PMT = \frac{25000 \times 0.06}{(1 + 0.06)^{20} - 1}
   \]
   Now, let's calculate this.

I'll compute it next.Melinda should set aside approximately **$679.61** at the end of each year to ensure she has $25,000 for the roof replacement in 20 years, given a 6% annual interest rate.

In this case, we calculated the **future value of an ordinary annuity**, as the payments are made annually with the goal of reaching a specific future sum.

### Do you want further details, or have any questions about this?

Here are 5 related questions:
1. What if the interest rate was different, say 5% or 7%?
2. How does the compounding frequency (monthly vs yearly) affect the amount?
3. What if Melinda decided to make monthly instead of yearly contributions?
4. How would this change if she wanted the funds in 15 or 25 years?
5. What happens if she starts saving after 5 years instead of immediately?

**Tip**: Always ensure to account for the impact of interest rates when planning long-term savings—small changes in rates can significantly affect outcomes.

Melinda has recently purchased a house and expects that the roof will need replacement in 20 years, which will cost approximately $25,000. To ensure she has the necessary funds for this future expense, she plans to save an equal sum of money at the end of each year. Her savings will be invested and will accrue a 6% annual interest rate. What is the amount she should set aside annually for this purpose, and should you calculate the future value or present value or annuity?

Learn how to calculate the annual amount Melinda needs to save for a $25,000 roof replacement in 20 years, with a 6% interest rate. This step-by-step guide walks through the future value of an ordinary annuity formula and provides a clear solution. Suitable for high school students and beyond.

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