5. A loan for Nu 10,000 is to be repaid in monthly payments of Nu 300. What is the balance on the loan after each period of time, if the interest rate is 14% p.a. compounded monthly?

a) One month
b) Two months



Answer :

To determine the balance on a loan of Nu 10,000 after making monthly payments of Nu 300 with an annual interest rate of 14% compounded monthly, we will address each month individually.

### a) Balance after one month

1. Calculate the monthly interest rate:
Since the interest is compounded monthly, we divide the annual interest rate by 12.
[tex]\[ \text{Monthly interest rate} = \frac{14\%}{12} = \frac{0.14}{12} \approx 0.01167 \text{ (or 1.167% per month)} \][/tex]

2. Calculate the interest accrued for the first month:
The interest for the first month is calculated by multiplying the loan amount by the monthly interest rate.
[tex]\[ \text{Interest for one month} = 10,000 \times 0.01167 \approx 116.67 \][/tex]

3. Determine the new balance before any payment:
Add the interest to the initial loan amount.
[tex]\[ \text{New balance before payment} = 10,000 + 116.67 = 10,116.67 \][/tex]

4. Subtract the monthly payment to get the new balance:
After making the payment of Nu 300, the new balance is:
[tex]\[ \text{Balance after one month} = 10,116.67 - 300 \approx 9,816.67 \][/tex]

Therefore, the balance on the loan after one month is approximately Nu 9,816.67.

### b) Balance after two months

1. Calculate the interest accrued for the second month:
Now, we calculate the interest based on the new balance (Nu 9,816.67).
[tex]\[ \text{Interest for second month} = 9,816.67 \times 0.01167 \approx 114.52 \][/tex]

2. Determine the new balance before any payment:
Add the interest to the balance after one month.
[tex]\[ \text{New balance before payment} = 9,816.67 + 114.52 \approx 9,931.19 \][/tex]

3. Subtract the monthly payment to get the new balance:
After making the second monthly payment of Nu 300, the new balance is:
[tex]\[ \text{Balance after two months} = 9,931.19 - 300 \approx 9,631.19 \][/tex]

Therefore, the balance on the loan after two months is approximately Nu 9,631.19.

In summary, the balance remaining on the loan after:
- One month is approximately Nu 9,816.67.
- Two months is approximately Nu 9,631.19.