To determine the rate of compound interest per year when the compound interest for a principal amount of Rs. 100 over one year is Rs. 12, follow these steps:
1. Identify the given values:
- Principal amount (P): Rs. 100
- Compound Interest (CI): Rs. 12
- Time period (T): 1 year
2. Recall the formula for compound interest when compounded annually:
[tex]\[
\text{CI} = P \left(1 + \frac{R}{100}\right)^T - P
\][/tex]
Where:
- CI is the compound interest
- P is the principal amount
- R is the rate of interest per year
- T is the time period in years
3. Insert the given values into the compound interest formula:
[tex]\[
12 = 100 \left(1 + \frac{R}{100}\right)^1 - 100
\][/tex]
4. Simplify the equation:
[tex]\[
12 = 100 \left(1 + \frac{R}{100}\right) - 100
\][/tex]
[tex]\[
12 = 100 + 100 \left(\frac{R}{100}\right) - 100
\][/tex]
[tex]\[
12 = 100 + R - 100
\][/tex]
5. Solve for R:
[tex]\[
12 = R
\][/tex]
6. Since R is obtained directly as 12, the rate of interest is 12%.
Therefore, the rate of compound interest per year that results in Rs. 12 compound interest for a principal of Rs. 100 in one year is:
[tex]\[
\boxed{12\%}
\][/tex]
