Future Value Annuity
1. **State the problem:** You save R2525 every month at the end of each month for 3 years. The bank pays 13.5% interest per annum compounded monthly. You want to find out how much money you can withdraw at the end of 3 years.
2. **Identify the variables:**
- Monthly payment, $P = 2525$
- Annual interest rate, $r = 13.5\% = 0.135$
- Number of years, $t = 3$
- Number of months, $n = 3 \times 12 = 36$
- Monthly interest rate, $i = \frac{r}{12} = \frac{0.135}{12} = 0.01125$
3. **Use the future value of an ordinary annuity formula:**
$$FV = P \times \frac{(1 + i)^n - 1}{i}$$
4. **Calculate the future value:**
$$FV = 2525 \times \frac{(1 + 0.01125)^{36} - 1}{0.01125}$$
5. Calculate $(1 + 0.01125)^{36}$:
$$1.01125^{36} \approx 1.488864$$
6. Substitute back:
$$FV = 2525 \times \frac{1.488864 - 1}{0.01125} = 2525 \times \frac{0.488864}{0.01125}$$
7. Simplify:
$$ \frac{0.488864}{0.01125} \approx 43.432$$
8. Final value:
$$FV = 2525 \times 43.432 \approx 109,640.8$$
**Answer:** You can withdraw approximately $109,640.80$ at the end of 3 years.