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.

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 = $18 \times 900 = \text{Ksh. } 16,200$
Total hire purchase price = Deposit + Total amount from installments
Total hire purchase price = $10,000 + 16,200 = \text{Ksh. } 26,200$

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) = $20,000 - 10,000 = \text{Ksh. } 10,000$

Interest paid = Total hire purchase price - Cash price
Interest paid = $26,200 - 20,000 = \text{Ksh. } 6,200$

The accumulated amount is the principal plus the interest paid.
A = P + Interest paid
A = $10,000 + 6,200 = \text{Ksh. } 16,200$

The interest is compounded semi-annually, so $n=2$.
The period is 18 months, which is $t = \frac{18}{12} = 1.5$ years.
The compound interest formula is $A = P\left(1 + \frac{r}{n}\right)^{nt}$.

Divide both sides by 10,000:

Take the cube root of both sides:

Subtract 1 from both sides:

Multiply by 2:

Convert to a percentage and round to 1 decimal place:

The rate of interest per annum is $\boxed{\text{34.9\%}}$.