Calculating Compound Interest Period

We need to find the time period (T) for a given principal amount, interest rate, and compound interest earned.

Given Information:

• Principal (P) = ₹20,000
• Rate (R) = 8% per annum
• Compound Interest (CI) = ₹3,328

Compound Interest Formula:

The formula for the Amount (A) when interest is compounded annually is:

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

Also, the Compound Interest is calculated as:

$CI = A - P$

Step-by-Step Calculation:

1. Calculate the total Amount (A):

   $A = P + CI$

   $A = 20000 + 3328 = 23328$

2. Substitute the values of A, P, and R into the Amount formula:

   $23328 = 20000 \left(1 + \frac{8}{100}\right)^T$

3. Simplify the equation:

   $23328 = 20000 \left(1 + 0.08\right)^T$

   $23328 = 20000 \left(1.08\right)^T$

4. Isolate the term with T:

   $\frac{23328}{20000} = \left(1.08\right)^T$

   $1.1664 = \left(1.08\right)^T$

5. Determine the value of T by inspection or calculation. We check powers of 1.08:

   $(1.08)^1 = 1.08$

   $(1.08)^2 = 1.1664$

6. From the comparison, we find T:

   $T = 2$

Therefore, the period is 2 years.