Suppose you'd like to save enough money to pay cash for your next car. The goal is to save an extra $28,000
 over the next 6
 years. What amount must be deposited quarterly into an account that earns 5.3%
 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 regular deposits into an account with compound interest, also known as the future value of an ordinary annuity:

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

Where:
- $ FV $ is the future value, or the total amount after all the deposits.
- $ P $ is the regular deposit amount (what we are solving for).
- $ r $ is the interest rate per period.
- $ n $ is the total number of deposit periods.

### Step 1: Identify the values from the problem.
- $ FV = 28,000 $ (the target amount to save)
- The annual interest rate is 5.3%, so the quarterly interest rate is $ \frac{5.3\%}{4} = \frac{0.053}{4} = 0.01325 $.
- The number of quarters in 6 years is $ 6 \times 4 = 24 $ quarters.

### Step 2: Substitute these values into the formula.
\[
28,000 = P \times \frac{(1 + 0.01325)^{24} - 1}{0.01325}
\]

### Step 3: Solve for $ P $.
Now I'll calculate the result.The amount that must be deposited quarterly into the account is approximately **$998.63** to reach your goal of saving $28,000 over 6 years with a 5.3% interest rate, compounded quarterly.

Would you like more details on this calculation, or do you have any further questions?

Here are 5 related questions to expand on this topic:
1. How would the required deposit change if the interest rate increased to 6%?
2. What would happen if the deposits were made monthly instead of quarterly?
3. How much total interest will you earn over the 6 years?
4. What if the goal was $35,000 instead of $28,000, with the same interest rate?
5. How long would it take to reach $28,000 if you could only deposit $800 quarterly?

**Tip:** Compounding interest grows faster as the number of compounding periods increases, so shorter compounding intervals can significantly affect savings.

Suppose you'd like to save enough money to pay cash for your next car. The goal is to save an extra $28,000 over the next 6 years. What amount must be deposited quarterly into an account that earns 5.3% 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 $28,000 in 6 years with a 5.3% interest rate compounded quarterly. This problem covers compound interest calculations and future value of an ordinary annuity, suitable for Grades 11-12.

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