Compound interest on a certain sum of money at 20% per annum for 2 years is Rs. 5995. What is the simple interest on the same money at 8% per annum for 6 years?

Introduction / Context:
This question first gives us the compound interest on an unknown principal at a relatively high rate, and then asks for the simple interest on the same principal at a different rate and for a different period. We must determine the principal using the compound interest information and then use it to compute the new simple interest.

Given Data / Assumptions:

• Compound interest for 2 years at 20% per annum is Rs. 5995.
• Interest is compounded annually for this part.
• The same principal is then invested at 8% per annum simple interest for 6 years.
• We must find the simple interest for 6 years at 8% per annum on that principal.

Concept / Approach:

For compound interest, CI2 = P * [(1 + r / 100)^2 - 1]. We use this formula with r = 20% and CI2 = 5995 to find the principal P. Then we apply the simple interest formula SI = P * R * T / 100 with rate 8% and time 6 years to find the required simple interest.

Step-by-Step Solution:

Verification / Alternative check:

Why Other Options Are Wrong:

Values such as Rs. 5989, Rs. 7844, and Rs. 6789 do not follow from the correct principal and simple interest formula. They may arise from arithmetic mistakes or from confusing the two interest rates or time periods. Only Rs. 6540 is consistent with both the initial compound interest data and the simple interest calculation.

Common Pitfalls:

One common mistake is to treat the given compound interest as simple interest when solving for the principal, which leads to an incorrect P. Another error is to reuse the 20% rate instead of the new 8% rate when computing the simple interest. It is important to keep track of which rate and time correspond to each part of the problem.

Final Answer:

The simple interest on the same money at 8% per annum for 6 years is Rs. 6540.