Suppose you'd like to save enough money to pay cash for your next car. The goal is to save an extra $22,000
 over the next 6
 years. What amount must be deposited quarterly into an account that earns 4.9%
 interest, compounded quarterly, in order to reach your goal? Round your answer to the nearest cent, if necessary.

To solve this problem, we need to use the formula for the future value of a series of equal payments (an ordinary annuity), since the deposits are made quarterly and the interest is compounded quarterly.

The formula is:

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

Where:
- $ FV $ is the future value (the goal, \$22,000)
- $ P $ is the regular quarterly deposit amount (which we need to find)
- $ r $ is the interest rate per period
- $ n $ is the total number of periods

### Step 1: Identify the known values.
- $ FV = 22,000 $ (the future value we want to reach)
- Interest rate per year = 4.9%, so per quarter $ r = \frac{4.9\%}{4} = \frac{0.049}{4} = 0.01225 $
- The number of years = 6 years, and since we are making quarterly deposits, $ n = 6 \times 4 = 24 $ periods

### Step 2: Rearrange the formula to solve for $ P $.

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

### Step 3: Substitute the values into the formula.

\[
P = \frac{22,000 \times 0.01225}{(1 + 0.01225)^{24} - 1}
\]

Now, let's calculate this step-by-step.

The quarterly deposit needed to reach a future value of \$22,000 over 6 years, with a 4.9% interest rate compounded quarterly, is approximately **\$794.07**.

Would you like further details on any part of this solution? Here are some related questions you might explore:

1. What if the interest rate were higher or lower—how would the quarterly deposit change?
2. How much total interest would be earned over the 6 years?
3. What if the goal was to save in 5 years instead of 6?
4. How does changing the compounding period affect the required deposit?
5. What if instead of quarterly, the deposit was made monthly?

**Tip**: Compounding interest grows faster the more frequently it is compounded, making it important to understand how small changes in periods and rates affect savings.

Suppose you'd like to save enough money to pay cash for your next car. The goal is to save an extra $22,000 over the next 6 years. What amount must be deposited quarterly into an account that earns 4.9% interest, compounded quarterly, in order to reach your goal? Round your answer to the nearest cent, if necessary.

Find out how much you need to deposit quarterly to save $22,000 over 6 years, with a 4.9% interest rate compounded quarterly. Learn how the future value of annuities and compound interest formulas are applied in this scenario. Suitable for Grades 10-12.

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