A motorcycle costs Kshs 120,000. If a deposit of Kshs 40,000 is paid, and the balance is financed over 20 months at a simple interest rate of 18% p.a., calculate the total amount to be paid and the mo

The cash price of the motorcycle is Kshs 120,000.
The deposit paid is Kshs 40,000.
The balance to be financed is the cash price minus the deposit.

$$\text{Balance} = \text{Cash Price} - \text{Deposit}$$ $$\text{Balance} = 120,000 - 40,000 = \text{Kshs } 80,000$$

The simple interest rate is 18% per annum (p.a.).
The number of equal monthly installments is 20.
First, convert the installment period into years:

$$\text{Time (T)} = \frac{20 \text{ months}}{12 \text{ months/year}} = \frac{20}{12} \text{ years} = \frac{5}{3} \text{ years}$$

Now, use the simple interest formula: $SI = \frac{P \times R \times T}{100}$
Where:

$$P = \text{Principal (Balance)} = \text{Kshs } 80,000$$ $$R = \text{Rate} = 18\%$$ $$T = \text{Time} = \frac{5}{3} \text{ years}$$ $$SI = \frac{80,000 \times 18 \times \frac{5}{3}}{100}$$ $$SI = \frac{80,000 \times 18 \times 5}{100 \times 3}$$ $$SI = \frac{80,000 \times 6 \times 5}{100}$$ $$SI = \frac{80,000 \times 30}{100}$$ $$SI = 800 \times 30$$ $$SI = \text{Kshs } 24,000$$

This is the balance plus the total simple interest.

$$\text{Total Amount} = \text{Balance} + \text{Simple Interest}$$ $$\text{Total Amount} = 80,000 + 24,000 = \text{Kshs } 104,000$$

The total amount is to be paid in 20 equal monthly installments.

$$\text{Amount per Installment} = \frac{\text{Total Amount}}{\text{Number of Installments}}$$ $$\text{Amount per Installment} = \frac{104,000}{20}$$ $$\text{Amount per Installment} = \frac{10,400}{2}$$ $$\text{Amount per Installment} = \text{Kshs } 5,200$$

The amount of each installment is:

$$\text{Kshs } 5,200$$