The simple interest in 3 years and compound interest in 2 years on a certain sum of money at the same rate are Rs. 1200 and Rs. 832 respectively. The principal is?

• A) Rs. 7500
• B) Rs. 4000
• C) Rs. 3000
• D) Rs. 5000

To find the principal amount, we can use the information given about simple interest (SI) and compound interest (CI).

Understanding Simple Interest

The formula for simple interest is:

SI = (Principal × Rate × Time) / 100

Given that the simple interest for 3 years is Rs. 1200, we can express this as:

1200 = (P × R × 3) / 100

This simplifies to:

P × R = 40000 (Equation 1)

Understanding Compound Interest

The formula for compound interest is:

CI = P × (1 + R/100)^n - P

For 2 years, the compound interest is Rs. 832, so we can write:

832 = P × [(1 + R/100)^2 - 1]

This can be rearranged to:

P × [(1 + R/100)^2] = P + 832 (Equation 2)

Relating SI and CI

From Equation 1, we can express R in terms of P:

R = 40000 / P

Substituting R into Equation 2 gives us:

P × [(1 + (40000 / P) / 100)^2] = P + 832

Now, simplifying this will help us find the value of P.

Calculating the Principal

First, simplify the expression:

1 + (40000 / P) / 100 = 1 + 400 / P

Now, squaring this:

(1 + 400 / P)^2 = 1 + 800 / P + 160000 / P^2

Substituting back into the equation:

P × (1 + 800 / P + 160000 / P^2) = P + 832

This simplifies to:

P + 800 + 160000 / P = P + 832

Thus, we have:

800 + 160000 / P = 832

Rearranging gives:

160000 / P = 32

From this, we find:

P = 160000 / 32 = 5000

Final Answer

The principal amount is Rs. 5000, which corresponds to option D.