A customer buys a TV set on hire purchase for Ksh. 20,000. A deposit of Ksh. 10,000 is paid, and the balance is paid in 18 equal monthly installments of Ksh. 900. Calculate the annual interest rate.

You're on a roll — here's the solution to the hire purchase problem. Step 1: Calculate the total amount paid by the customer. The customer pays a deposit and then monthly installments. Deposit = Ksh. 10,000 Number of installments = 18 Amount per installment = Ksh. 900 Total amount from installments = 18 × 900 = Ksh. 16,200 Total hire purchase price = Deposit + Total amount from installments Total hire purchase price = 10,000 + 16,200 = Ksh. 26,200 Step 2: Calculate the principal amount on which interest is charged. The interest is charged on the balance after the deposit. Cash price of TV set = Ksh. 20,000 Principal (P) = Cash price - Deposit Principal (P) = 20,000 - 10,000 = Ksh. 10,000 Step 3: Calculate the total interest paid. Interest paid = Total hire purchase price - Cash price Interest paid = 26,200 - 20,000 = Ksh. 6,200 Step 4: Determine the accumulated amount (A) for the compound interest calculation. The accumulated amount is the principal plus the interest paid. A = P + Interest paid A = 10,000 + 6,200 = Ksh. 16,200 Step 5: Apply the compound interest formula and solve for the annual interest rate (r). The interest is compounded semi-annually, so n=2. The period is 18 months, which is t = (18)/(12) = 1.5 years. The compound interest formula is A = P(1 + (r)/(n))^nt. 16,200 = 10,000 (1 + (r)/(2))^2 × 1.5 16,200 = 10,000 (1 + (r)/(2))^3 Divide both sides by 10,000: (16,200)/(10,000) = (1 + (r)/(2))^3 1.62 = (1 + (r)/(2))^3 Take the cube root of both sides: [3]1.62 = 1 + (r)/(2) 1.17449... = 1 + (r)/(2) Subtract 1 from both sides: 0.17449... = (r)/(2) Multiply by 2: r = 0.17449... × 2 r = 0.34898... Convert to a percentage and round to 1 decimal place: r = 34.898...\% ≈ 34.9\% The rate of interest per annum is 34.9\%. What's next?