Simple Interest Rate Calculation

The problem states a 60% increase in an amount over 6 years at simple interest. This means the Simple Interest (SI) earned is 60% of the Principal (P).

SI = 60% of P = $0.60 \times P$

The formula for Simple Interest is:

$ SI = \frac{P \times R \times T}{100} $

Where:

• P = Principal amount
• R = Rate of interest per annum (%)
• T = Time period in years

Substituting the known values:

$ 0.60 \times P = \frac{P \times R \times 6}{100} $

We can cancel P from both sides:

$ 0.60 = \frac{R \times 6}{100} $

Solving for R:

$ R = \frac{0.60 \times 100}{6} $

$ R = \frac{60}{6} $

$ R = 10\% $

So, the annual interest rate is 10%.

Compound Interest Calculation

Now, we need to calculate the compound interest (CI) on ₹10,000 for 3 years at the same rate (10%).

Principal (P) = ₹10,000

Rate (R) = 10%

Time (T) = 3 years

The formula for the Amount (A) under compound interest is:

$ A = P \left(1 + \frac{R}{100}\right)^T $

Substituting the values:

$ A = 10000 \left(1 + \frac{10}{100}\right)^3 $

$ A = 10000 \left(1 + 0.1\right)^3 $

$ A = 10000 \left(1.1\right)^3 $

$ A = 10000 \times 1.331 $

$ A = 13310 $

The total amount after 3 years is ₹13,310.

The Compound Interest (CI) is the difference between the final amount and the principal:

$ CI = A - P $

$ CI = 13310 - 10000 $

$ CI = 3310 $

Therefore, the compound interest is ₹3,310.