Question

Joe applied a loan amount of K2500 with bsp at the rate of10%p.a and regular payment of K850 at the end of every year after the interest is credited. What is the amount owing after the second payment? Show your working out

Answer 1

To determine the amount owing after the second payment for Joe's loan, we will need to calculate the interest accrued after each year and then subtract the payments made.

**Loan Details:**
- Initial loan amount (Principal): \( P = K2500 \)
- Interest rate: \( r = 10\% = 0.10 \)
- Payment per year: \( PMT = K850 \)

### Year 1:

1. **Interest for Year 1:**
\[
\text{Interest Year 1} = P \times r = K2500 \times 0.10 = K250
\]

2. **Amount after Year 1:**
\[
\text{Total Amount after Year 1} = P + \text{Interest Year 1} = K2500 + K250 = K2750
\]

3. **Amount after First Payment:**
\[
\text{Amount after Payment 1} = \text{Total Amount after Year 1} - PMT = K2750 - K850 = K1900
\]

### Year 2:

1. **Interest for Year 2:**
\[
\text{Interest Year 2} = \text{Amount after Payment 1} \times r = K1900 \times 0.10 = K190
\]

2. **Amount after Year 2:**
\[
\text{Total Amount after Year 2} = \text{Amount after Payment 1} + \text{Interest Year 2} = K1900 + K190 = K2090
\]

3. **Amount after Second Payment:**
\[
\text{Amount after Payment 2} = \text{Total Amount after Year 2} - PMT = K2090 - K850 = K1240
\]

### Final Amount Owing After the Second Payment:
After the second payment, the amount owing is:
\[
\boxed{K1240}
\]