 loan of R15 080,00 is being repaid by 14 half-yearly payments, with the first payment made one half year after the loan is taken out. The interest rate is 9% per year. compounded half-yearly. The size of each of the half-yearly payments is R1 475,13. the outstanding principle after two years is

To find the outstanding principal after two years, we need to calculate the remaining balance on the loan after four payments (since two years corresponds to four half-year periods).

Given:
- Initial loan amount (Principal) = R15,080.00
- Half-yearly payments = R1,475.13
- Interest rate per year = 9%, compounded half-yearly, so the interest rate per half-year period = 9% / 2 = 4.5%
- Number of half-yearly payments = 14
- Payments made after 2 years = 4

### Step 1: Calculate the balance after 4 payments

The outstanding principal after each payment can be calculated using the formula for the outstanding balance of an amortizing loan:

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

Where:
- \( P \) is the outstanding principal after \(n\) payments.
- \( C \) is the payment amount (R1,475.13).
- \( i \) is the interest rate per period (4.5% = 0.045).
- \( n \) is the number of remaining payments after 2 years (14 - 4 = 10).

We can now compute the outstanding principal after 4 payments.The outstanding principal after two years (or after four half-yearly payments) is approximately **R11,672.29**.

Do you have any questions or would you like further details?

Here are five related questions for further exploration:
1. How much interest is paid in total after the full 14 payments?
2. What is the total amount paid over the life of the loan?
3. How does the outstanding balance change if the interest rate increases to 10% compounded half-yearly?
4. What is the balance after 10 payments have been made?
5. How much principal is repaid after the first year?

**Tip:** When dealing with amortizing loans, understanding the breakdown between interest and principal in each payment helps in planning for early repayment.

Learn how to calculate the outstanding principal after two years of repaying a loan of R15,080.00 with half-yearly payments of R1,475.13 at an interest rate of 9% per year, compounded half-yearly. Detailed step-by-step solution provided.

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