To find the future value ($FV$) of an annuity where deposits are made quarterly for 20 years at an interest rate of 3% per year, we use the formula for the future value of an ordinary annuity:

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

Where:

• $P$ is the amount deposited each period (in this case, $2,800),
• $r$ is the interest rate per period,
• $n$ is the total number of periods.

Step 1: Identify the values

• $P = 2,800$
• The annual interest rate is 3%, but since the deposits are quarterly, we divide this by 4 to get the quarterly interest rate: $r = \frac{3\%}{4} = \frac{0.03}{4} = 0.0075$
• The total number of periods is the number of quarters in 20 years: $n = 20 \times 4 = 80 \text{ quarters}$

Step 2: Plug the values into the formula

$FV = 2,800 \times \frac{(1 + 0.0075)^{80} - 1}{0.0075}$

Let's calculate that.

The accumulated future value (FV) of the annuity account is approximately $305,403.09.

Would you like more details on how this was calculated or have any further questions?

Here are 5 related questions for further practice:

1. What is the future value if the interest rate is increased to 4% per year?
2. How would the future value change if the deposits were made monthly instead of quarterly?
3. What is the present value of this annuity with the same parameters?
4. How much interest is earned over the 20-year period in this scenario?
5. What is the future value if deposits are made at the beginning of each period instead of at the end?

Tip: When dealing with annuities, the frequency of deposits and compounding plays a major role in determining the future value.