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The problem asks to find the future value of an annuity due, where payments are made at the beginning of each period, with interest compounded annually.

The given information is:
- $ R = 700 $ (the payment amount per period),
- $ i = 0.03 $ (the interest rate per period),
- $ n = 6 $ (the number of periods).

### Formula for Future Value of an Annuity Due:
The formula for the future value of an annuity due is:

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

Where:
- $ FV $ is the future value,
- $ R $ is the regular payment,
- $ i $ is the interest rate per period,
- $ n $ is the number of periods.

### Step-by-step Calculation:

1. Plug in the given values into the formula:
\[
FV = 700 \times \frac{(1 + 0.03)^6 - 1}{0.03} \times (1 + 0.03)
\]

2. Calculate $ (1 + 0.03)^6 $:
\[
(1.03)^6 = 1.194052
\]

3. Subtract 1:
\[
1.194052 - 1 = 0.194052
\]

4. Divide by $ i $ (0.03):
\[
\frac{0.194052}{0.03} = 6.4684
\]

5. Multiply by $ R $ (700):
\[
700 \times 6.4684 = 4527.88
\]

6. Multiply by $ (1 + i) $ (1.03):
\[
4527.88 \times 1.03 = 4663.72
\]

So, the future value of the annuity due is **\$4663.72**.

---

Would you like any more details or clarification?

Here are 5 related questions you could explore:
1. How would the future value change if the interest rate increased?
2. What is the difference between an annuity due and an ordinary annuity?
3. How would this calculation change if interest were compounded monthly instead of annually?
4. How can we determine the present value of an annuity due?
5. What effect would increasing the number of periods have on the future value?

**Tip:** Remember, for an annuity due, payments are made at the start of each period, which leads to a slightly higher future value than an ordinary annuity.

Find the future value of the following annuity due. Assume that interest is compounded annually, there are n payments of R dollars, and the interest rate is i. R = 700; i = 0.03; n = 6

Learn how to calculate the future value of an annuity due with a payment of $700, an interest rate of 3%, and 6 periods, with step-by-step calculations using the future value formula for an annuity due. Ideal for college or university-level students.

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