Question

If the compound interest for 2 years at 10% per annum is Rs.1050, then the principal amount is

• A. Rs.5000
• B. Rs.5500
• C. Rs.6000
• D. Rs.6500

Hint:

For 2-year compound interest, use $(1 + R/100)^2 - 1$ shortcut.

Answer 1

The Correct Option is A

To find the principal amount when the compound interest for 2 years at 10% per annum is given as Rs. 1050, we can use the formula for compound interest, which is:

\(A = P\left(1 + \frac{r}{100}\right)^n\)

where \(A\) is the amount after \(n\) years, \(P\) is the principal, \(r\) is the rate of interest, and \(n\) is the number of years.

Given:

• Compound Interest (CI) = Rs. 1050
• Rate of interest, \(r = 10\%\)
• Time, \(n = 2\) years

The relationship between compound interest and amount is:

\(CI = A - P\)

Substituting the compound interest formula, we get:

\(A = P + CI\)

Using the compound amount formula:

\(A = P\left(1 + \frac{10}{100}\right)^2 = P\left(1.1\right)^2\)

Now, \(A = P + 1050\)

Substitute \(A\) from both equations:

\(P\left(1.1\right)^2 = P + 1050\)

\(P(1.21) = P + 1050\)

Rearrange the equation to solve for \(P\):

\(1.21P - P = 1050\)

\(0.21P = 1050\)

\(P = \frac{1050}{0.21}\)

\(P = 5000\)

Thus, the principal amount is Rs. 5000.