Calculate Time using Simple Interest

The first step is to determine the time period ('t' years) using the information provided about simple interest. We are given the principal amount, the simple interest accrued, and the rate of interest.

The formula for Simple Interest (SI) is:

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

Let's list the known values:

• Principal Amount (P) = Rs. 14,000
• Simple Interest (SI) = Rs. 1,260
• Rate of Interest (R) = 3% per annum
• Time (T) = ? years

Substitute these values into the simple interest formula:

1260 = \frac{14000 \times 3 \times t}{100}

To simplify, we can cancel out the zeros in the denominator:

1260 = 140 \times 3 \times t

Calculate the product of 140 and 3:

1260 = 420 \times t

Now, solve for 't' by dividing the simple interest by 420:

t = \frac{1260}{420}

t = 3

So, the time period for which the simple interest was calculated is 3 years.

Calculate Compound Interest

With the time period determined as 3 years, we now need to calculate the compound interest on the same principal amount (Rs. 14,000) but at a different interest rate (10% per annum) compounded annually.

The formula to calculate the Amount (A) after compound interest is applied is:

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

Here are the values we will use:

• Principal Amount (P) = Rs. 14,000
• Rate of Interest (R) = 10% per annum
• Time (t) = 3 years

Plug these values into the compound interest formula:

A = 14000 \left(1 + \frac{10}{100}\right)^3

Simplify the term inside the parenthesis:

A = 14000 \left(1 + 0.1\right)^3

A = 14000 \left(1.1\right)^3

First, calculate (1.1)^3:

(1.1)^3 = 1.1 \times 1.1 \times 1.1 = 1.331

Now, multiply this result by the principal amount to find the total Amount (A):

A = 14000 \times 1.331

A = 18634

The Compound Interest (CI) is the difference between the final Amount (A) and the initial Principal (P):

CI = A - P

CI = 18634 - 14000

CI = 4634

Therefore, the compound interest accrued on the amount is Rs. 4,634.