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To find the future value of the ordinary annuity, we can use the formula:

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

where:
- \( R \) is the regular payment amount,
- \( i \) is the interest rate per period,
- \( n \) is the total number of periods.

From the image, we have:
- \( R = 7000 \)
- \( i = 0.06 \) (annual interest rate)
- \( n = 20 \) (number of years)

### Calculation:
1. Substitute the values:
   \[
   FV = 7000 \times \frac{(1 + 0.06)^{20} - 1}{0.06}
   \]

2. Calculate \( (1 + 0.06)^{20} \):
   \[
   (1.06)^{20} \approx 3.207135
   \]

3. Subtract 1 from this value:
   \[
   3.207135 - 1 = 2.207135
   \]

4. Divide by the interest rate \( i \):
   \[
   \frac{2.207135}{0.06} \approx 36.78558333
   \]

5. Multiply by the regular payment \( R \):
   \[
   FV = 7000 \times 36.78558333 \approx 257499.0833
   \]

Rounding to the nearest cent, the future value of the ordinary annuity is:
\[
\boxed{257,499.08}
\]

Would you like more details or have any further questions?

### Related Questions:
1. What would the future value be if the interest rate was 8% instead of 6%?
2. How does the future value change if the payments are made semi-annually instead of annually?
3. Can you explain how compounding frequency affects the future value of an annuity?
4. What is the difference between an ordinary annuity and an annuity due?
5. How would you calculate the present value of the same annuity?

### Tip:
When solving annuity problems, always ensure the compounding period matches the payment frequency. If not, adjust the interest rate and number of periods accordingly.

Find the future value of the ordinary annuity. Interest is compounded annually. R = 7000; i = 0.06; n = 20.

This problem involves calculating the future value of an ordinary annuity, given a regular payment of 7000, an annual interest rate of 6%, and a period of 20 years. It covers key mathematical concepts such as annuities and compound interest, using the formula FV = R × ((1 + i)^n - 1) / i. Suitable for Grades 11-12.

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