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.