Use the savings plan formula to answer the following question. 

At age 

3838​, 

you start saving for retirement. If your investment plan pays an APR of 

44​% 

and you want to have 

​$1.21.2 

million when you retire in 

2727 

​years, how much should you deposit​ monthly?

Question content area bottom

Part 1

You should invest 

​$enter your response here 

each month.

​(Do not round until the final answer. Then round to two decimal places as​ needed.)

We will use the **savings plan formula** to calculate the required monthly deposit.

The formula for the future value of a savings plan is:

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

Where:
- $A$ = Future value (desired retirement amount) = $1,200,000
- $P$ = Monthly deposit (what we are solving for)
- $r$ = Annual interest rate (APR) = 4% = 0.04
- $n$ = Number of compounding periods per year (monthly compounding, so $n = 12$)
- $t$ = Number of years = 27 years

Now, we can substitute the values into the formula and solve for $P$. First, rearrange the formula to isolate $P$:

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

Let's calculate this step by step. I'll compute the monthly deposit $P$.The required monthly deposit to reach $1.2 million in 27 years with a 4% APR is approximately **$2062.50**.

Would you like more details on how this was calculated, or have any other questions?

Here are some related questions to consider:
1. What happens to the monthly deposit if the APR increases to 5%?
2. How much would you need to deposit annually instead of monthly to reach the same goal?
3. How much total money will you have deposited by the end of 27 years?
4. What would happen if the retirement time frame is reduced by 5 years?
5. How much would your savings grow with no monthly deposit but an initial lump sum investment?

**Tip:** Starting retirement savings early, even with smaller amounts, can significantly reduce how much you need to deposit monthly!

At age 38, you start saving for retirement. If your investment plan pays an APR of 4% and you want to have $1.2 million when you retire in 27 years, how much should you deposit monthly? (Do not round until the final answer. Then round to two decimal places as needed.)

Discover how to calculate the required monthly deposit to reach $1.2 million in 27 years with an APR of 4%. Using the compound interest savings plan formula, this solution provides a step-by-step breakdown. Perfect for students in Grades 11-12.

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