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.
### 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.
