Question

joe applied a loan amount of K2500 with bsp at the rate of 10% p.a and regular payment of K850 at the end of every year after the interest is credited. What is the final repayment amount. Show your working out.

Answer 1

To calculate the final repayment amount of Joe's loan, we can break it down into steps. We will consider how the loan interest accumulates, the impact of the annual payments, and continue this process until the loan is fully repaid.

### Initial Loan Amount:
- Principal (Loan Amount), \( P = K2500 \)
- Annual Interest Rate, \( r = 10\% = 0.10 \)
- Annual Payment, \( A = K850 \)

### Yearly Calculation:

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

2. **Total Amount at End of Year 1 Before Payment**:
\[
\text{Total} = P + \text{Interest} = K2500 + K250 = K2750
\]

3. **After Payment**:
\[
\text{Remaining Balance} = K2750 - K850 = K1900
\]

#### Year 2:
1. **Interest for Year 2**:
\[
\text{Interest} = K1900 \times 0.10 = K190
\]

2. **Total Amount at End of Year 2 Before Payment**:
\[
\text{Total} = K1900 + K190 = K2090
\]

3. **After Payment**:
\[
\text{Remaining Balance} = K2090 - K850 = K1240
\]

#### Year 3:
1. **Interest for Year 3**:
\[
\text{Interest} = K1240 \times 0.10 = K124
\]

2. **Total Amount at End of Year 3 Before Payment**:
\[
\text{Total} = K1240 + K124 = K1364
\]

3. **After Payment**:
\[
\text{Remaining Balance} = K1364 - K850 = K514
\]

#### Year 4:
1. **Interest for Year 4**:
\[
\text{Interest} = K514 \times 0.10 = K51.40
\]

2. **Total Amount at End of Year 4 Before Payment**:
\[
\text{Total} = K514 + K51.40 = K565.40
\]

3. **After Payment**:
\[
\text{Remaining Balance} = K565.40 - K850 = K0 \text{ (as payment exceeds the balance)}
\]

Since Joe has fully paid off the loan and covered the interest up until the last payment in year 4, we can summarize the payments made:

### Total Payments Made:
- Year 1: K850
- Year 2: K850
- Year 3: K850
- Year 4: K850 (only part covered interest)

Total repayments over the years = \( K850 \times 4 = K3400 \)

However, since we paid slightly over the remaining amount on year 4 (K565.40), we do not count the excess.

### Final Repayment Amount:
So, the final sum of all payments until the loan was cleared = K3400. Joe effectively pays K3400 in total for a loan of K2500.

**Final Repayment Amount**: **K3400 (includes the interest paid)**.