Use the savings plan formula to answer the following question.
Your goal is to create a college fund for your child. Suppose you find a fund that offers an APR of 7%. How much should you deposit monthly to accumulate ​$81 comma 81,000 in 18 ​years?
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Part 1
You should invest ​$enter your response here each month.
​(Do not round until the final answer. Then round to two decimal places as​ needed.)

The savings plan formula is typically used to calculate how much needs to be deposited periodically to reach a certain amount after a given number of periods, under compound interest. The formula for periodic deposits is:

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

Where:
- $A$ is the future value (the amount you want to accumulate),
- $P$ is the monthly deposit,
- $r$ is the annual interest rate (expressed as a decimal),
- $n$ is the number of compounding periods per year,
- $t$ is the number of years.

Given:
- $A = 81,000$ (the target amount),
- $r = 0.07$ (7% annual interest rate),
- $n = 12$ (since deposits are monthly),
- $t = 18$ years.

We need to solve for $P$, the monthly deposit. Let's substitute the values and rearrange the formula to solve for $P$:

\[
81,000 = P \times \frac{(1 + 0.07/12)^{12 \times 18} - 1}{0.07/12}
\]

I will calculate the value of $P$.The monthly deposit you need to make is approximately **$188.06** to accumulate $81,000 in 18 years, given a 7% annual interest rate.

Would you like further details or clarification on any part of the calculation?

Here are 5 related questions to consider:
1. How does changing the interest rate affect the monthly deposit?
2. What happens if the compounding frequency changes from monthly to annually?
3. How much would you need to deposit each month if the goal was to reach $100,000 in 18 years?
4. How can an increase in the number of years affect the monthly payment?
5. What if you want to achieve the same goal in 15 years instead of 18?

**Tip**: Starting savings early significantly reduces the required monthly deposit, thanks to compound interest!

Your goal is to create a college fund for your child. Suppose you find a fund that offers an APR of 7%. How much should you deposit monthly to accumulate $81,000 in 18 years?

Discover how much to deposit monthly to accumulate $81,000 over 18 years with a 7% APR using the savings plan formula. Learn about compound interest, periodic deposits, and step-by-step calculations. Perfect for students and financial planners.

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