To calculate the future value of equal payments made at the end of every six months, we can use the same formula as before:

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

Given:

• Payment ($P$) = R2,907

• Annual interest rate = 13.5%

• Interest compounded half-yearly, so the interest rate per period ($r$) is:

  $r = \frac{13.5\%}{2} = 6.75\% = 0.0675$

• 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, let's calculate the future value ($FV$).

$FV = 2,907 \times \frac{(1 + 0.0675)^8 - 1}{0.0675}$

I'll compute this now.The future value of the equal payments of R2,907 made every six months for 4 years, at an interest rate of 13.5% per annum compounded half-yearly, is approximately R29,558.03.

Would you like further details or have any questions?

Here are some related questions:

1. How does increasing the payment amount affect the future value?
2. What would the future value be if the interest rate was 15% per annum?
3. How is the future value calculated if payments are made at the beginning of each period?
4. What is the impact of compounding frequency on the future value?
5. How would the future value differ if payments were made annually instead of semi-annually?
6. How do you calculate the present value of these payments?
7. What is the effect of extending the payment period to 5 years?
8. How does a decrease in the interest rate to 10% affect the future value?

Tip: Always ensure that the interest rate and the number of periods correspond to the compounding frequency when calculating future values.