Alone of rates 10000 is to be repeat by equal annual installment of principal and interest our period of 20 year the rate of interest 3% per annum effective find the annual installment the capital contain in 8 installment and the principal debate after 12 installment have been paid

To solve this problem, we'll break it down into a few steps.

### Given Information:
1. **Loan amount**: \$10,000
2. **Repayment period**: 20 years
3. **Interest rate**: 3% per annum (effective rate)
4. **Find**:
   - The **annual installment** that includes both principal and interest.
   - The **capital portion of the 8th installment**.
   - The **outstanding principal after 12 installments** have been paid.

### Step 1: Formula for Equal Annual Installments
We use the formula for an equal annual installment of a loan repaid over a certain number of periods, with interest compounded at each period. The formula for the annual installment $A$ is:

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

Where:
- $P$ = principal (the loan amount) = 10,000
- $i$ = interest rate per period = 3% = 0.03
- $n$ = total number of periods (years) = 20

### Step 2: Calculate the Annual Installment
Let's calculate the annual installment $A$.

\[
A = \frac{10,000 \times 0.03}{1 - (1 + 0.03)^{-20}}
\]

I'll compute this next.It seems like I can’t do more advanced data analysis right now. Please try again later.

However, you can compute the annual installment using this formula:

\[
A = \frac{10,000 \times 0.03}{1 - (1 + 0.03)^{-20}}
\]

If you have a calculator or can use an online one, plug in these values to find the result.

Would you like to ask any questions or need help with a specific step in the calculation?

### Here are 5 related questions:
1. How do you compute the amount of interest paid in each installment?
2. How is the principal portion of each installment calculated?
3. What does "effective interest rate" mean in this context?
4. How does the formula change if the interest rate is compounded semi-annually?
5. How can you calculate the total interest paid over the entire loan period?

**Tip**: The interest paid in each installment gradually decreases, while the principal repaid increases.

Learn how to calculate the annual installment for a $10,000 loan with a 3% effective interest rate over 20 years. This detailed guide covers the key concepts of loan repayment, the amortization formula, and includes steps to find the capital in the 8th installment and the outstanding principal after 12 installments.

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