There is a 60% increase in an amount in 6 years at simple interest. Using the same rate of interest, what will be the compound interest on Rs 12000 after 3 years, if interest is compounded annually?

Introduction:
This problem links simple interest and compound interest. First, you must deduce the annual rate of simple interest from the information about a 60% increase over 6 years. Then, using the same rate, you compute the compound interest on a new principal over 3 years.

Given Data / Assumptions:

• Under simple interest, an amount increases by 60% in 6 years.
• We infer the annual rate from this information.
• We then consider a principal P = Rs 12000.
• Time for compound interest calculation = 3 years.
• Same annual rate is used, with annual compounding.

Concept / Approach:
If an amount increases by 60% in 6 years under simple interest, then total simple interest over 6 years is 60% of the principal. This gives SI = 0.60P = P * r * 6 / 100, allowing us to find r. Then we use the compound interest formula A = P * (1 + r/100)^3 for P = 12000 and obtain CI = A − P.

Step-by-Step Solution:
Let the original principal be P (for the 60% increase information).Total SI over 6 years = 0.60P.Using SI formula: SI = P * r * 6 / 100 = 0.60P.Thus P cancels, giving r * 6 / 100 = 0.60.So r = 0.60 * 100 / 6 = 10% per annum.Now consider P = Rs 12000 at 10% compound interest for 3 years.A = 12000 * (1 + 10/100)^3 = 12000 * (1.1)^3.(1.1)^3 = 1.331, so A = 12000 * 1.331 = Rs 15972.Compound interest CI = A − P = 15972 − 12000 = Rs 3972.

Verification / Alternative Check:
You may also compute CI year by year. First year interest: 12000 * 10% = 1200 (amount 13200). Second year interest: 13200 * 10% = 1320 (amount 14520). Third year interest: 14520 * 10% = 1452 (amount 15972). Total CI = 1200 + 1320 + 1452 = 3972, in agreement with the formula result.

Why Other Options Are Wrong:
Rs 4972 and Rs 5972: These overestimate the compound interest that would accrue at 10% per annum on Rs 12000 for 3 years.Rs 2972 and Rs 3672: These underestimate the true compound interest, possibly due to mixing up simple and compound interest calculations.

Common Pitfalls:
One frequent mistake is to treat the 60% increase as directly giving the 10% rate without showing the algebra, which can be error prone if adapted to other numbers. Another is to continue using the simple interest formula when computing the interest on Rs 12000, thereby missing the compounding effect.

Final Answer:
The compound interest on Rs 12000 after 3 years at the same rate is Rs 3972.