Brian Bell & Co. is selling micro-oven for K4000 by cash. If this item is purchased on an installments basis where the method of repayment is to deposit K500 followed by equal semi-annually repayments of K900 for three years.

(a) Calculate the flat rate of interest charged if this item is bought on an installments basis.

(b) Calculate the total amount paid at the end of 3 years if this item is bought on installments basis.

To solve this problem, we will calculate the total cost paid through installments and compare it with the cash price to determine the flat rate of interest. Let's break down the problem step-by-step.

### Given Information
- **Cash price of the micro-oven**: K4000
- **Down payment**: K500
- **Installment payments**: K900 each, semi-annually
- **Duration of installments**: 3 years

### Step 1: Calculate the Total Amount Paid via Installments

The installment payments are made semi-annually for 3 years. This means there are:

\[
\text{Number of semi-annual payments} = 3 \text{ years} \times 2 = 6 \text{ payments}
\]

Each payment is K900, so the total paid through installments is:

\[
\text{Total installment amount} = 6 \times K900 = K5400
\]

Including the down payment, the total amount paid is:

\[
\text{Total amount paid} = K500 + K5400 = K5900
\]

### Step 2: Calculate the Total Interest Paid

The interest paid is the difference between the total amount paid through installments and the cash price:

\[
\text{Interest paid} = \text{Total amount paid} - \text{Cash price}
\]

\[
\text{Interest paid} = K5900 - K4000 = K1900
\]

### Step 3: Calculate the Flat Rate of Interest

The flat rate of interest is calculated based on the original principal amount and the total interest paid. The original principal amount in this case is the cash price minus the down payment:

\[
\text{Principal amount} = K4000 - K500 = K3500
\]

The flat rate of interest is then calculated as follows:

\[
\text{Flat rate of interest} = \frac{\text{Interest paid}}{\text{Principal amount} \times \text{Number of years}}
\]

\[
\text{Flat rate of interest} = \frac{K1900}{K3500 \times 3}
\]

\[
\text{Flat rate of interest} = \frac{K1900}{K10500}
\]

\[
\text{Flat rate of interest} \approx 0.18095 \approx 18.1\%
\]

### Summary of Answers

**(a) The flat rate of interest charged if this item is bought on an installment basis is approximately 18.1%.**

**(b) The total amount paid at the end of 3 years if this item is bought on an installment basis is K5900.**

Would you like more details or have any other questions?

### Related Questions
1. What would the flat rate of interest be if the down payment was K1000 instead of K500?
2. How does the interest rate change if the installment payments are made monthly instead of semi-annually?
3. What would be the impact on the flat rate of interest if the duration of the loan was extended to 5 years?
4. How much interest would be saved if the item was purchased for cash instead of through installments?
5. What is the annual effective interest rate for this installment plan?

### Tip
When dealing with installment plans, always compare the total amount paid through installments with the cash price to understand the cost of financing.

Learn how to calculate the flat rate of interest and total amount paid over 3 years for a micro-oven purchased on installments from Brian Bell & Co. Includes step-by-step calculation details and comparison with cash purchase.

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