After paying a deposit, buyer acquired a refrigerator by agreeing to pay the remaining balance of K2500 in fortnightly installments at 10% per annum over a period of 30 months. Calculate the fortnightly installments 

To calculate the fortnightly installment for the refrigerator purchase, we need to use the formula for calculating the payment amount on a loan with fixed payments. Since the payment frequency is fortnightly (every two weeks), we need to adjust the interest rate and the number of periods accordingly.

### Step 1: Identify the variables
- **Principal (P)**: K2500
- **Annual interest rate (r)**: 10% (which is 0.10 as a decimal)
- **Number of years (t)**: 30 months = 2.5 years
- **Number of payments per year**: Since the payments are fortnightly, there are 26 payments per year.
- **Total number of payments (n)**: \( 26 \times 2.5 = 65 \) payments

### Step 2: Adjust the interest rate for the payment period
The interest rate per period is calculated as:
\[
i = \frac{r}{26} = \frac{0.10}{26} \approx 0.003846
\]

### Step 3: Calculate the fortnightly installment
The formula to calculate the installment is:
\[
PMT = \frac{P \times i}{1 - (1 + i)^{-n}}
\]
where:
- \( P \) is the principal,
- \( i \) is the interest rate per period,
- \( n \) is the total number of payments.

Substituting the values:
\[
PMT = \frac{2500 \times 0.003846}{1 - (1 + 0.003846)^{-65}}
\]

Now, let's calculate it step by step.

### Step 4: Solve the equation

\[
1 + i = 1 + 0.003846 = 1.003846
\]
\[
(1.003846)^{-65} \approx 0.7912
\]
\[
1 - 0.7912 \approx 0.2088
\]
\[
PMT \approx \frac{2500 \times 0.003846}{0.2088} \approx \frac{9.615}{0.2088} \approx 46.04
\]

### Final Answer:
The fortnightly installment is approximately **K46.04**.

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Would you like more details on this calculation or have any other questions?

### Related Questions:
1. How does the interest rate affect the installment amount?
2. What would the installment be if the interest rate was 5% instead of 10%?
3. How would changing the payment period from 30 months to 36 months impact the installments?
4. What would be the total amount paid after 30 months?
5. How is the formula for calculating installments derived?
6. What happens if you miss a payment in such an installment plan?
7. How can one calculate the total interest paid over the loan period?
8. What is the difference between simple interest and compound interest?

### Tip:
Always double-check the frequency of payments when calculating loan installments, as it significantly impacts the interest rate applied and the number of payments.

Learn how to calculate fortnightly installments for a refrigerator purchase agreement, where the buyer pays a deposit and the remaining balance of K2500 over 30 months at 10% annual interest. Detailed step-by-step solution provided.

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