Question

A has deposited some amount in a bank. The bank gives 10% compound interest. If he receives Rs.24200 at the end of two years, the amount deposited initially in the bank is

• A. Rs.21000
• B. Rs.20000
• C. Rs.22000
• D. Rs.22200

Hint:

For a 10% rate compounded annually for 2 years, the effective interest rate is:
\[ 10 + 10 + \frac{10 \times 10}{100} = 21\% \]
Thus, the total accumulated amount is 121% of the principal.
If 121% of $P = 24200$, then 1% of $P = 200$, and the 100% principal $P = 20000$.

Answer 1

The Correct Option is B

Step 1: Understanding the Question:
This problem is based on Compound Interest ($CI$).
We are given:
- Accumulated Amount ($A$) received at the end of two years = Rs.24200
- Rate of compound interest ($R$) = 10% per annum
- Time period ($n$) = 2 years
We need to determine the initial amount deposited, which is the Principal ($P$).

Step 2: Key Formula or Approach:
The compound interest amount formula is:
\[ A = P \left(1 + \frac{R}{100}\right)^n \]
Rearranging the formula to solve for the Principal ($P$):
\[ P = \frac{A}{\left(1 + \frac{R}{100}\right)^n} \]

Step 3: Detailed Calculation:
Substitute the given values into the formula:
- $A = 24200$
- $R = 10$
- $n = 2$
\[ P = \frac{24200}{\left(1 + \frac{10}{100}\right)^2} \]
Simplify the term inside the bracket:
\[ 1 + \frac{10}{100} = 1 + 0.1 = 1.1 \]
Calculate the square of 1.1:
\[ (1.1)^2 = 1.21 \]
Substitute this value back into the equation:
\[ P = \frac{24200}{1.21} \]
To make division easier, eliminate the decimal point in the denominator by multiplying both numerator and denominator by 100:
\[ P = \frac{24200 \times 100}{121} \]
Notice that $242 \div 121 = 2$. Therefore, $24200 \div 121 = 200$:
\[ P = 200 \times 100 \]
\[ P = 20000 \]
Thus, the initially deposited principal amount is Rs.20000.

Step 4: Final Answer:
The initial deposit is Rs.20000, which corresponds to Option (B).