Calculate the future value of equal payments of R2,334 paid at the end of every six months for 4 years. Interest is 12.3% per annum compounded half yearly

To calculate the future value of equal payments made at the end of every six months, we can use the formula for the future value of an annuity:

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

Where:
- \(FV\) is the future value of the annuity.
- \(P\) is the payment amount per period.
- \(r\) is the interest rate per period.
- \(n\) is the total number of periods.

Given:
- Payment (\(P\)) = R2,334
- Annual interest rate = 12.3%
- Interest compounded half-yearly, so the interest rate per period (\(r\)) is:
  
  \[
  r = \frac{12.3\%}{2} = 6.15\% = 0.0615
  \]

- Total time = 4 years, with payments made every 6 months. Therefore, the total number of periods (\(n\)) is:

  \[
  n = 4 \times 2 = 8 \text{ periods}
  \]

Now, we can calculate the future value (\(FV\)).

\[
FV = 2,334 \times \frac{(1 + 0.0615)^8 - 1}{0.0615}
\]

Let's calculate this step-by-step.

1. Calculate \((1 + r)^n\):
   \[
   (1 + 0.0615)^8 = 1.0615^8
   \]

2. Subtract 1 from the result:
   \[
   (1.0615^8) - 1
   \]

3. Divide by \(r = 0.0615\):
   \[
   \frac{(1.0615^8) - 1}{0.0615}
   \]

4. Multiply the result by the payment amount \(P = 2,334\).

Now, I'll compute this.The future value of the equal payments of R2,334 made every six months for 4 years, at an interest rate of 12.3% per annum compounded half-yearly, is approximately **R23,225.44**.

Would you like more details or have any questions?

Here are some related questions:

1. How would the future value change if the payments were made monthly?
2. What if the interest was compounded quarterly instead of half-yearly?
3. How does the future value compare if the interest rate is reduced to 10% per annum?
4. What is the present value of these payments at the same interest rate?
5. How do varying interest rates affect the future value of an annuity?
6. What is the difference between annuities and perpetuities?
7. How can this formula be applied in a financial planning context?
8. What is the impact of inflation on the future value of these payments?

**Tip:** When dealing with annuities, always check whether the payments are made at the beginning or the end of each period, as this affects the calculation.

Learn how to calculate the future value of equal payments of R2,334 paid at the end of every six months for 4 years at 12.3% interest compounded semi-annually. Step-by-step solution provided.

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