Zandile borrowed money from a bank and she is repaying the loan by making monthly payments of R1348 at the end of every month, each payment includes interest and repayment of the principle. The loan will be paid off in 9 years and interest is calculated at a rate of 12.123% per year, compounded monthly. What is the interest component of the 7th payment of the 4th year?

To solve this problem, we need to break it into steps using the formula for loan amortization, which accounts for both the interest and the principal components in each monthly payment.

### Given information:
- Monthly payment: \( R1348 \)
- Loan term: 9 years (i.e., 9 × 12 = 108 months)
- Interest rate: 12.123% per year, compounded monthly. Thus, monthly interest rate \( i = \frac{12.123\%}{12} = 1.01025\% \) or 0.0101025 as a decimal.

We are asked to find the interest component of the **7th payment of the 4th year**. This corresponds to the **7th payment of month 3 × 12 + 7 = 43rd payment** overall.

#### Step 1: Find the original loan amount.
We can use the formula for the present value of an annuity, since the monthly payments are constant:

\[
PV = P \times \frac{1 - (1 + i)^{-n}}{i}
\]

Where:
- \( PV \) is the loan amount (principal),
- \( P = 1348 \) is the monthly payment,
- \( i = 0.0101025 \) is the monthly interest rate,
- \( n = 108 \) is the total number of payments.

Let's calculate the present value (loan amount):

\[
PV = 1348 \times \frac{1 - (1 + 0.0101025)^{-108}}{0.0101025}
\]

#### Step 2: Calculate the balance before the 43rd payment.
The balance after each payment can be calculated using the formula for the remaining balance of a loan:

\[
B_m = P \times \frac{1 - (1 + i)^{m-n}}{i}
\]

Where \( m \) is the month of the payment (43 in this case).

#### Step 3: Find the interest component.
The interest component for the 43rd payment is calculated by multiplying the remaining balance after the 42nd payment by the monthly interest rate:

\[
I_{43} = B_{42} \times i
\]

#### Step 4: Breakdown of Payment.
The total payment (R1348) is split between the interest component \( I_{43} \) and the principal repayment. After finding the interest component, subtract it from R1348 to find the principal portion.

Would you like me to compute the exact values step by step?

Zandile borrowed money from a bank and she is repaying the loan by making monthly payments of R1348 at the end of every month, each payment includes interest and repayment of the principle. The loan will be paid off in 9 years and interest is calculated at a rate of 12.123% per year, compounded monthly. What is the interest component of the 7th payment of the 4th year?

Learn how to calculate the interest component of the 7th payment of the 4th year for a loan of R1348 per month, repaid over 9 years at an interest rate of 12.123% per annum, compounded monthly. This example covers loan amortization and compound interest concepts, suitable for Grades 11-12.

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