Charlotte sets aside $110 each month in an account bearing 4% interest, compounded monthly. How much will she have saved after 7 years?

To solve this problem, we use the formula for the future value of a series of regular deposits (also called an annuity). The formula is:

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

Where:
- $ A $ is the amount in the account after $ t $ years.
- $ P $ is the monthly deposit amount.
- $ r $ is the annual interest rate (expressed as a decimal).
- $ n $ is the number of times the interest is compounded per year.
- $ t $ is the number of years.

### Given:
- $ P = 110 $ (monthly deposit)
- $ r = 0.04 $ (4% annual interest rate)
- $ n = 12 $ (compounded monthly)
- $ t = 7 $ years

### Now, we plug in the values:

\[
A = 110 \times \frac{(1 + 0.04/12)^{12 \times 7} - 1}{0.04/12}
\]

I'll calculate this.Charlotte will have saved approximately **$10,642.96** after 7 years, with $110 deposited monthly at 4% interest compounded monthly.

Would you like further details on this calculation or any additional questions?

Here are some related questions:
1. What if Charlotte deposited $200 instead of $110 each month?
2. How much would she save in 10 years under the same conditions?
3. How would the savings change if the interest rate was 5% instead of 4%?
4. What if the interest was compounded quarterly instead of monthly?
5. How does the formula for compound interest differ from the future value of an annuity?

**Tip:** Increasing the frequency of compounding (e.g., monthly to daily) can slightly increase the future value due to more frequent application of interest.

Learn how to calculate the future value of monthly savings of $110 over 7 years in an account with 4% interest compounded monthly. This guide covers the annuity formula for calculating compound interest, exponential growth, and how interest accumulation affects savings. Suitable for Grades 10-12.

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