How much should you deposit at the end of each quarter into an account that pays  4.4% annual interest compounded quarterly in order to have $5000 in three years? 

To determine how much should be deposited at the end of each quarter to accumulate $5000 in three years with a 4.4% annual interest rate compounded quarterly, we can use the formula for the future value of an annuity:

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

Where:
- $ FV $ = future value (the amount you want, $5000),
- $ P $ = deposit amount (what we're solving for),
- $ r $ = annual interest rate (4.4% or 0.044),
- $ n $ = number of times the interest is compounded per year (quarterly means $ n = 4 $),
- $ t $ = number of years (3 years).

### Step-by-step process:
1. Substitute the values:
   \[
   5000 = P \times \frac{(1 + 0.044/4)^{4 \times 3} - 1}{0.044/4}
   \]
2. Simplify the equation and solve for $ P $.

Let's calculate this.The amount you should deposit at the end of each quarter is approximately **$392.06** to accumulate $5000 in three years with a 4.4% annual interest rate compounded quarterly.

Do you want further details or have any questions about this calculation?

Here are some related questions to explore further:
1. What would the deposit be for a different future value, say $10,000?
2. How would the result change with monthly compounding instead of quarterly?
3. What if the interest rate was higher, such as 6%?
4. How does increasing the deposit period to 5 years affect the outcome?
5. How can the formula for future value of an annuity be derived?

**Tip:** Compounding frequency significantly affects the growth of your savings, as more frequent compounding leads to greater accumulated interest.

How much should you deposit at the end of each quarter into an account that pays 4.4% annual interest compounded quarterly in order to have $5000 in three years?

Find out how much you need to deposit quarterly to reach a future value of $5000 in 3 years, with an annual interest rate of 4.4% compounded quarterly. This detailed guide covers the future value of an annuity formula and step-by-step calculations. Suitable for high school students and anyone learning about compound interest.

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