1. **Problem:** Mr. Sarfo borrowed 25000 at 21% simple interest per annum for 3 years but repaid in 2 equal yearly installments. Find the yearly payment. 2. **Formula:** Simple Interest $I = P \times r \times t$ where $P$ is principal, $r$ rate, $t$ time. 3. Calculate total interest: $$I = 25000 \times 0.21 \times 3 = 15750$$ 4. Total amount to repay: $$A = P + I = 25000 + 15750 = 40750$$ 5. Since he paid in 2 equal installments, yearly payment: $$\text{Yearly payment} = \frac{40750}{2} = 20375$$ 6. **Answer:** Mr. Sarfo paid 20375 each year. --- 1. **Problem:** Given $t = m\sqrt{n^2 + 4r}$, (i) make $n$ the subject. 2. Square both sides: $$t^2 = m^2 (n^2 + 4r)$$ 3. Divide both sides by $m^2$: $$\frac{t^2}{\cancel{m^2}} = \cancel{m^2} (n^2 + 4r) \Rightarrow \frac{t^2}{m^2} = n^2 + 4r$$ 4. Isolate $n^2$: $$n^2 = \frac{t^2}{m^2} - 4r$$ 5. Take positive root: $$n = \sqrt{\frac{t^2}{m^2} - 4r}$$ --- 1. **Problem:** (ii) Find positive $n$ when $t=25$, $m=5$, $r=4$. 2. Substitute values: $$n = \sqrt{\frac{25^2}{5^2} - 4 \times 4} = \sqrt{\frac{625}{25} - 16} = \sqrt{25 - 16} = \sqrt{9}$$ 3. Calculate: $$n = 3$$ --- **Final answers:** - Yearly payment = 20375 - $n$ as subject: $n = \sqrt{\frac{t^2}{m^2} - 4r}$ - Positive $n$ value = 3