Use the savings plan formula to answer the following question. 

You put 

​$300300 

per month in an investment plan that pays an APR of 

4.54.5​%. 

How much money will you have after 

2727 

​years? Compare this amount to the total deposits made over the time period.

Question content area bottom

Part 1

After 

2727 

years the investment plan will contain 

​$enter your response here.

To calculate the amount of money you will have after 27 years in the savings plan, we will use the **future value of a savings plan formula**:

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

Where:
- $ FV $ = future value of the investment
- $ P $ = monthly deposit ($300 per month)
- $ r $ = annual interest rate (4.5% or 0.045 in decimal form)
- $ n $ = number of times the interest is compounded per year (monthly, so $ n = 12 $)
- $ t $ = number of years (27 years)

### Step 1: Plug the values into the formula.

\[
FV = 300 \times \frac{(1 + \frac{0.045}{12})^{12 \times 27} - 1}{\frac{0.045}{12}}
\]

Now let's calculate it. I'll perform the calculation to get the future value.The future value of your investment after 27 years will be approximately **$189,011.52**.

### Part 2: Compare to the total deposits made.

Now, let's calculate the total deposits. The total amount deposited is simply the monthly deposit multiplied by the number of months:

\[
\text{Total Deposits} = P \times n \times t
\]

Let me calculate that for you.The total amount you will have deposited over 27 years is **$97,200**.

### Summary:
- **Future value** of the investment after 27 years: **$189,011.52**
- **Total deposits** made: **$97,200**

Thus, your investment plan will grow significantly due to interest, earning you approximately **$91,811.52** in interest over the 27 years.

Would you like further details or have any questions?

Here are 5 related questions to explore:
1. How does increasing the APR affect the future value of the investment?
2. What happens if you increase the monthly deposit to $400 instead of $300?
3. How would the total amount change if the investment period were extended to 30 years?
4. What effect would a change to quarterly compounding have on the final amount?
5. What is the impact of inflation on the future value of investments over long periods?

**Tip:** Small increases in the interest rate or deposit amount can significantly boost the future value of your savings over long periods due to compounding.

You put $300 per month in an investment plan that pays an APR of 4.5%. How much money will you have after 27 years? Compare this amount to the total deposits made over the time period.

Learn how to calculate the future value of a savings plan with monthly deposits of $300 and an APR of 4.5% over 27 years. Compare the future value to the total deposits made, with detailed calculations and explanations. Suitable for high school students studying compound interest and savings plans.

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