1. Stating the problem: Siya wants to accumulate R 100000 in 20 years by depositing monthly payments into a trust fund that earns 12% annual interest, compounded monthly. 2. We recognize this as a future value of an ordinary annuity problem. The formula for the future value $FV$ after making monthly payments $P$ for $n$ months at a monthly interest rate $i$ is: $$FV = P \times \frac{(1+i)^n - 1}{i}$$ 3. Given: - $FV = 100000$ - Annual interest rate = 12%, so monthly rate $i = \frac{12\%}{12} = 1\% = 0.01$ - Number of years $= 20$, number of months $n = 20 \times 12 = 240$ 4. Substitute the known values into the formula to solve for $P$: $$100000 = P \times \frac{(1+0.01)^{240} - 1}{0.01}$$ 5. Calculate $(1+0.01)^{240}$: $$ (1.01)^{240} = e^{240 \times \ln(1.01)} \approx e^{240 \times 0.00995} = e^{2.388} \approx 10.883$$ 6. Compute numerator for fraction: $$10.883 - 1 = 9.883$$ 7. The fraction is: $$\frac{9.883}{0.01} = 988.3$$ 8. Now solve for $P$: $$P = \frac{100000}{988.3} \approx 101.2$$ 9. Therefore, Siya needs to pay approximately $\boxed{101.2}$ per month to reach R 100000 in 20 years.