Compound Interest Time Calculation

This problem requires finding the time period (in years) for a given principal amount to grow to a specific amount at a fixed compound interest rate.

Given Information:

• Principal (P) = ₹4,000
• Amount (A) = ₹4,840
• Rate of Interest (R) = 10% per annum
• Time (T) = ? years

Compound Interest Formula Application

The formula for compound interest is:

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

Where:

• A = Amount
• P = Principal
• R = Rate of Interest
• T = Time in years

Calculating the Time Period

Substitute the given values into the formula:

$4840 = 4000 \left(1 + \frac{10}{100}\right)^T$

Simplify the expression inside the parenthesis:

$4840 = 4000 \left(1 + 0.10\right)^T$

$4840 = 4000 (1.10)^T$

Now, isolate the term with T:

$\frac{4840}{4000} = (1.10)^T$

Simplify the fraction:

$1.21 = (1.10)^T$

Recognize that $1.21$ is the square of $1.10$:

$1.10 \times 1.10 = 1.21$

Therefore:

$ (1.10)^2 = (1.10)^T $

By comparing the exponents, we find the time period:

$ T = 2 $

So, it will take 2 years for the sum to increase from ₹4,000 to ₹4,840 at 10% compound interest.