To determine the compound interest on a principal amount of ₹312,121 over 2 years at an annual interest rate of 12%, we can use the compound interest formula. Here's the step-by-step process:
### 1. Understanding the Variables:
- Principal (P): ₹312,121
- Annual Interest Rate (r): 12% (or 0.12 in decimal form)
- Time (t): 2 years
- Number of Times Interest is Compounded Per Year (n): Since it is compounded annually, \( n = 1 \)
### 2. Compound Interest Formula:
The formula to calculate compound interest when compounded annually is given by:
[tex]\[ CI = P \left(1 + \frac{r}{n}\right)^{nt} - P \][/tex]
### 3. Plugging in the Values:
Substitute the variables into the formula:
[tex]\[ CI = 312121 \left(1 + \frac{0.12}{1}\right)^{1 \times 2} - 312121 \][/tex]
### 4. Simplifying the Expression:
First, calculate the term inside the parentheses:
[tex]\[ 1 + \frac{0.12}{1} = 1 + 0.12 = 1.12 \][/tex]
Now raise this to the power of \( nt \):
[tex]\[ (1.12)^{2} \][/tex]
Calculate \(1.12\) raised to the power of \(2\):
[tex]\[ (1.12)^2 = 1.2544 \][/tex]
Next, multiply the principal amount by this result:
[tex]\[ 312121 \times 1.2544 \][/tex]
### 5. Further Calculation:
[tex]\[ 312121 \times 1.2544 = 391524.5824 \][/tex]
Now, subtract the principal amount from this result to find the compound interest:
[tex]\[ 391524.5824 - 312121 = 79403.5824 \][/tex]
### 6. Final Result:
The compound interest on ₹312,121 over 2 years at an annual interest rate of 12% is approximately ₹79,403.58.
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So, the answer is ₹79,403.58.
