Certainly! To find the simple interest rate when Rs. 20000 amounts to Rs. 21200 in 6 months, we can follow these steps:
### Step 1: Identify the Given Values
- Principal (P): Rs. 20000
- Amount (A): Rs. 21200
- Time (T): 6 months, which we need to convert into years
### Step 2: Calculate the Interest Earned
The interest earned ([tex]\( I \)[/tex]) is the difference between the amount and the principal.
[tex]\[ I = A - P \][/tex]
[tex]\[ I = 21200 - 20000 \][/tex]
[tex]\[ I = 1200 \, \text{Rs} \][/tex]
### Step 3: Convert Time into Years
Since the time is given in months, and interest rates are typically calculated per annum (year), we need to convert 6 months into years.
[tex]\[ T = \frac{6}{12} \][/tex]
[tex]\[ T = 0.5 \, \text{years} \][/tex]
### Step 4: Use the Simple Interest Formula to Find the Rate
The formula for simple interest is:
[tex]\[ I = P \times R \times T \][/tex]
where [tex]\( R \)[/tex] is the rate of interest per annum.
Rearranging the formula to solve for [tex]\( R \)[/tex]:
[tex]\[ R = \frac{I}{P \times T} \][/tex]
We already have:
- [tex]\( I = 1200 \, \text{Rs} \)[/tex]
- [tex]\( P = 20000 \, \text{Rs} \)[/tex]
- [tex]\( T = 0.5 \, \text{years} \)[/tex]
Substituting these values into the formula:
[tex]\[ R = \frac{1200}{20000 \times 0.5} \][/tex]
[tex]\[ R = \frac{1200}{10000} \][/tex]
[tex]\[ R = 0.12 \][/tex]
To express [tex]\( R \)[/tex] as a percentage, we multiply by 100:
[tex]\[ R = 0.12 \times 100 \][/tex]
[tex]\[ R = 12\% \][/tex]
### Step 5: Conclusion
The rate of simple interest is:
[tex]\[ \boxed{12\%} \][/tex]
