The cash price of a music system is kshs. 30,000. It can be bought under hire purchase terms by paying a deposit of kshs. 10,000 and twelve monthly installments of Kshs. 3,200 per month. Determine the percentage rate of interest per month.

The total amount paid includes the deposit and all monthly installments.

$$\text{Total HP amount} = \text{Deposit} + (\text{Number of installments} \times \text{Monthly installment})$$ $$\text{Total HP amount} = \text{Kshs. } 10,000 + (12 \times \text{Kshs. } 3,200)$$ $$\text{Total HP amount} = \text{Kshs. } 10,000 + \text{Kshs. } 38,400$$ $$\text{Total HP amount} = \text{Kshs. } 48,400$$

The total interest is the difference between the total hire purchase amount and the cash price.

$$\text{Total interest} = \text{Total HP amount} - \text{Cash price}$$ $$\text{Total interest} = \text{Kshs. } 48,400 - \text{Kshs. } 30,000$$ $$\text{Total interest} = \text{Kshs. } 18,400$$

This is the principal amount on which the interest is charged, which is the cash price minus the deposit.

$$\text{Amount financed} = \text{Cash price} - \text{Deposit}$$ $$\text{Amount financed} = \text{Kshs. } 30,000 - \text{Kshs. } 10,000$$ $$\text{Amount financed} = \text{Kshs. } 20,000$$

The monthly interest rate is the total interest as a percentage of the amount financed, divided by the number of months.

$$\text{Monthly interest rate} = \frac{\text{Total interest}}{\text{Amount financed}} \times \frac{1}{\text{Number of months}} \times 100\%$$ $$\text{Monthly interest rate} = \frac{\text{Kshs. } 18,400}{\text{Kshs. } 20,000} \times \frac{1}{12} \times 100\%$$ $$\text{Monthly interest rate} = 0.92 \times \frac{1}{12} \times 100\%$$ $$\text{Monthly interest rate} = \frac{92}{12}\%$$ $$\text{Monthly interest rate} = \frac{23}{3}\%$$ $$\text{Monthly interest rate} \approx 7.67\%$$

The percentage rate of interest per month is approximately 7.67%.

The final answer is $\boxed{7.67\%}$.