The Hire Purchase (H.P.) price of a public address system was Ksh 276 000. A deposit of Ksh 60 000 was paid followed by 18 equal monthly instalments. The cash price of the public address system was 10

$$\text{Amount to be paid in instalments} = \text{H.P. price} - \text{Deposit}$$ $$\text{Amount to be paid in instalments} = 276000 \text{ Ksh} - 60000 \text{ Ksh}$$ $$\text{Amount to be paid in instalments} = 216000 \text{ Ksh}$$

$$\text{Monthly instalment} = \frac{\text{Amount to be paid in instalments}}{\text{Number of instalments}}$$ $$\text{Monthly instalment} = \frac{216000 \text{ Ksh}}{18}$$ $$\text{Monthly instalment} = 12000 \text{ Ksh}$$

The monthly instalment is:

$$\boxed{12000 \text{ Ksh}}$$

price.

$$\text{Cash price} = \text{H.P. price} - (10\% \text{ of H.P. price})$$ $$\text{Cash price} = 276000 \text{ Ksh} - \left(\frac{10}{100} \times 276000 \text{ Ksh}\right)$$ $$\text{Cash price} = 276000 \text{ Ksh} - 27600 \text{ Ksh}$$ $$\text{Cash price} = 248400 \text{ Ksh}$$

The cash price is:

$$\boxed{248400 \text{ Ksh}}$$

b) A customer decided to buy the system in cash and was allowed a 5% discount on the cash price. He took a bank loan to buy the system in cash. The bank charged compound interest on the loan at the rate of 20% p.a. The loan was repaid in 2 years. Calculate the amount repaid to the bank by the end of the second year.

$$\text{Discounted Cash Price} = \text{Cash Price} - (5\% \text{ of Cash Price})$$ $$\text{Discounted Cash Price} = 248400 \text{ Ksh} - \left(\frac{5}{100} \times 248400 \text{ Ksh}\right)$$ $$\text{Discounted Cash Price} = 248400 \text{ Ksh} - 12420 \text{ Ksh}$$ $$\text{Discounted Cash Price} = 235980 \text{ Ksh}$$

Here, $P = 235980 \text{ Ksh}$, $R = 20\%$, and $n = 2$ years.

$$A = 235980 \left(1 + \frac{20}{100}\right)^2$$ $$A = 235980 (1 + 0.20)^2$$ $$A = 235980 (1.20)^2$$ $$A = 235980 \times 1.44$$ $$A = 339811.20 \text{ Ksh}$$

The amount repaid to the bank by the end of the second year is:

$$\boxed{339811.20 \text{ Ksh}}$$

$$\text{Difference} = \text{Amount repaid to bank} - \text{H.P. price}$$ $$\text{Difference} = 339811.20 \text{ Ksh} - 276000 \text{ Ksh}$$ $$\text{Difference} = 63811.20 \text{ Ksh}$$

$$\text{Percentage} = \frac{\text{Difference}}{\text{H.P. price}} \times 100\%$$ $$\text{Percentage} = \frac{63811.20 \text{ Ksh}}{276000 \text{ Ksh}} \times 100\%$$ $$\text{Percentage} = 0.2312 \times 100\%$$ $$\text{Percentage} = 23.12\%$$

The percentage is:

$$\boxed{23.12\%}$$