This problem requires the calculation of the final amount on an investment using the formula for compound interest.
Step 1: Understanding the Question:
We need to find the total amount (Principal + Interest) after 2 years for a principal of Rs10,000 at a 10% annual compound interest rate.
Step 2: Key Formula or Approach: }
The formula for the amount (A) in compound interest is:
\[ A = P \left(1 + \frac{r}{n}\right)^{nt} \]
Where:
P = Principal amount (Rs10,000)
r = Annual interest rate (10% or 0.10)
n = Number of times interest is compounded per year (annually, so n=1)
t = Number of years (2)
Step 3: Detailed Explanation:
Substitute the given values into the formula:
\[ A = 10000 \left(1 + \frac{0.10}{1}\right)^{1 \times 2} \]
\[ A = 10000 (1 + 0.10)^2 \]
\[ A = 10000 (1.1)^2 \]
\[ A = 10000 \times 1.21 \]
\[ A = 12100 \]
The total amount after 2 years will be Rs12,100.
Alternatively, we can calculate year by year:
Interest for Year 1: 10% of Rs10,000 = Rs1,000.
Amount at the end of Year 1 = Rs10,000 + Rs1,000 = Rs11,000.
Interest for Year 2: 10% of Rs11,000 = Rs1,100.
Amount at the end of Year 2 = Rs11,000 + Rs1,100 = Rs12,100.
Step 4: Final Answer: }
The total amount after 2 years is Rs12,100.