A young teacher wants to start saving for her retirement.  She anticipates that she will be working for another 23 years and would like to have $1,000,000 saved by the time she retires.   If her investment will earn an average of 5.4%, how much does she need to save every year in order to reach her retirement goal?  Round your answer to the nearest whole number.  

To determine how much the teacher needs to save annually to reach her retirement goal of $1,000,000, we can use the formula for the **future value of an ordinary annuity**. The formula is:

\[
FV = P \times \frac{(1 + r)^n - 1}{r}
\]

Where:
- $ FV $ is the future value (in this case, $1,000,000),
- $ P $ is the annual payment (the unknown value we are solving for),
- $ r $ is the annual interest rate (5.4% = 0.054),
- $ n $ is the number of years (23 years).

We can rearrange the formula to solve for $ P $:

\[
P = \frac{FV \times r}{(1 + r)^n - 1}
\]

Substituting the values:

\[
P = \frac{1,000,000 \times 0.054}{(1 + 0.054)^{23} - 1}
\]

Let’s calculate this step by step.

1. Calculate $ (1 + r)^{n} $:

\[
(1 + 0.054)^{23} = 1.054^{23} \approx 3.315
\]

2. Subtract 1 from this value:

\[
3.315 - 1 = 2.315
\]

3. Now multiply $ FV \times r $:

\[
1,000,000 \times 0.054 = 54,000
\]

4. Finally, divide this result by $ 2.315 $:

\[
P = \frac{54,000}{2.315} \approx 23,319
\]

Thus, the teacher needs to save approximately **$23,319** per year to reach her retirement goal.

Would you like more details on any of the steps? Here are five related questions to explore further:

1. How would the annual savings change if the interest rate increased to 6%?
2. What would happen if she saved monthly instead of yearly?
3. How much interest will she earn in total over the 23 years?
4. What if she wants to retire with $1,200,000 instead of $1,000,000?
5. How would starting with an initial investment affect the yearly contribution?

**Tip:** The earlier you start saving, the less you'll need to contribute each year due to the power of compound interest!

A young teacher wants to start saving for her retirement. She anticipates that she will be working for another 23 years and would like to have $1,000,000 saved by the time she retires. If her investment will earn an average of 5.4%, how much does she need to save every year in order to reach her retirement goal? Round your answer to the nearest whole number.

Learn how to calculate the annual savings needed to reach $1,000,000 for retirement in 23 years, with an average interest rate of 5.4%. This step-by-step solution involves compound interest and the future value of annuities, ideal for students in Grades 10-12.

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