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: Recall the Compound Interest formula.
Amount = P x (1 + R/100)^n, where P = Principal, R = annual interest rate, n = number of years.
Step 2: Substitute the given values.
\[ 24200 = P \times \left(1 + \frac{10}{100}\right)^2 = P \times (1.1)^2 = P \times 1.21 \]
Step 3: Solve for P.
\[ P = \frac{24200}{1.21} = 20000 \] \[ \boxed{Rs.20000} \]