Janine is 21 years old. She opens an account that pays 1.25% interest, compounded monthly. She sets a goal of saving $10,000 by the time she is 24 years old. How much must she deposit each month?

This is a problem of calculating the monthly deposit required to meet a future value goal in an account with compound interest. We can use the **future value of a series formula** for compound interest to solve this problem.

The formula for the future value of a series of monthly deposits is:

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

Where:
- $FV$ is the future value (the amount Janine wants to save, which is $10,000).
- $P$ is the monthly deposit (what we need to find).
- $r$ is the annual interest rate (1.25%, or 0.0125).
- $n$ is the number of times the interest is compounded per year (monthly, so $n = 12$).
- $t$ is the time in years (from 21 to 24 years old, so $t = 3$).

### Step 1: Rearrange the formula to solve for $P$:
\[
P = \frac{FV \times r/n}{(1 + r/n)^{nt} - 1}
\]

### Step 2: Substitute the known values:
\[
P = \frac{10,000 \times 0.0125/12}{(1 + 0.0125/12)^{12 \times 3} - 1}
\]

Let's calculate the monthly deposit.Janine must deposit approximately **$272.75** each month in order to save $10,000 by the time she is 24 years old, with an account paying 1.25% interest compounded monthly.

Would you like more details or have any questions about this solution?

Here are five related questions to explore further:
1. How would the required monthly deposit change if the interest rate increased to 2%?
2. How much would Janine have saved if she started saving at age 22 instead of 21?
3. What if Janine only wanted to save $8,000 by age 24—how would the monthly deposit change?
4. How much total interest will Janine earn over the 3 years?
5. If the interest were compounded quarterly instead of monthly, how would that affect the monthly deposit?

**Tip:** Small changes in the interest rate or deposit period can have a noticeable impact on the total savings required!

Discover how to calculate the monthly deposit Janine needs to save $10,000 by age 24 with a 1.25% interest rate compounded monthly. This detailed solution covers the compound interest formula, step-by-step calculations, and key algebraic concepts. Perfect for students in Grades 9-12.

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