To calculate the future value of equal payments made at the end of each period, 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 (R2,324).
• $r$ is the interest rate per period.
• $n$ is the total number of payments.

Given:

• $P = R2,324$
• Annual interest rate = 13.8% → Half-yearly interest rate $r = \frac{13.8\%}{2} = \frac{0.138}{2} = 0.069$
• Number of years = 4 years → $n = 4 \times 2 = 8$ periods (since payments are made every six months)

Now, let's calculate the future value $FV$.The future value of the equal payments of R2,324 made every six months for 4 years, with an interest rate of 13.8% per annum compounded half-yearly, will be approximately R23,758.08.

Would you like further details or have any questions about this calculation?

Here are some related questions:

1. How would the future value change if the interest rate were 10%?
2. What is the total amount paid over the 4 years?
3. How does compounding frequency affect the future value?
4. What if payments were made quarterly instead of half-yearly?
5. How does the future value change with different payment amounts?
6. What if the payment was R3,000 instead of R2,324?
7. How can this calculation be adjusted for payments made at the beginning of each period?
8. What is the impact of making a lump sum payment at the end of the 4 years?

Tip: Understanding how compounding affects the future value of annuities can help in planning for long-term savings or investment goals.