Question

A certain sum of money earns a simple interest of ₹ 800 over 2-year period. The same sum of money invested at the same rate of interest and same period on a compound interest basis earns an interest of ₹ 900. What is the sum?

• A. ₹1,200
• B. ₹1,600
• C. ₹2,000
• D. ₹2,400

Answer 1

The Correct Option is B

To solve this problem, we need to compare the simple interest (SI) and compound interest (CI) formulas and solve for the principal amount.

Given that the simple interest earned after 2 years is ₹800, we use the simple interest formula:

\(SI = \frac{P \times R \times T}{100}\) 

Where:

• \(P\) = Principal
• \(R\) = Rate of interest per annum
• \(T\) = Time (years)

Next, we consider the compound interest, where the compound interest earned after 2 years is ₹900.

The compound interest formula is:

\(CI = P \times \left(1 + \frac{R}{100}\right)^T - P\)

From the given, we have:

\(900 = P \times \left(1 + \frac{R}{100}\right)^2 - P\)

We can rearrange this equation to:

\(900 = P \left[\left(1 + \frac{R}{100}\right)^2 - 1\right]\)

We can set this as Equation 2.

Now we have two equations:

• Equation 1: \(800 = \frac{P \times R \times 2}{100}\)
• Equation 2: \(900 = P \left[\left(1 + \frac{R}{100}\right)^2 - 1\right]\)

Check with options: Assume \(P = 1600\), \(R = 25\) which satisfies both simple and compound interest calculations directly.

With \(P = 1600\), we validate \(SI\) and \(CI\):

\(800 = \frac{1600 \times 25 \times 2}{100}\)

\(900 = 1600 \left[\left(1 + \frac{25}{100}\right)^2 - 1\right]\)

After solving (mathematical simplification), both conditions are satisfied. Hence, the option

₹1,600

1. .

 

Thus, the principal sum is ₹1,600.