Compound Interest Time Calculation

The problem asks for the time period ($n$) required for an investment to grow from a principal amount (P) to a final amount (A) at a given annual interest rate (R), compounded annually.

• Principal ($P$): ₹$1,000$
• Amount ($A$): ₹$1,331$
• Annual Interest Rate ($R$): $10\%$
• Time ($n$): ?

Compound Interest Formula

The formula for compound interest is:

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

Solving for Time Period

Substitute the given values into the formula:

$ 1,331 = 1,000 \left(1 + \frac{10}{100}\right)^n $

Simplify the expression:

$ 1,331 = 1,000 \left(1 + 0.10\right)^n $

$ 1,331 = 1,000 (1.1)^n $

Isolate the term with the exponent:

$ \frac{1,331}{1,000} = (1.1)^n $

$ 1.331 = (1.1)^n $

Recognize the relationship between $1.331$ and $1.1$. We know that $1.1 \times 1.1 = 1.21$ and $1.21 \times 1.1 = 1.331$. Therefore:

$ (1.1)^3 = 1.331 $

Equating the two expressions:

$ (1.1)^n = (1.1)^3 $

By comparing the exponents, we find the time period:

$ n = 3 $

So, the time required is $3$ years.

Final Answer

The time required for ₹$1,000$ to become ₹$1,331$ at $10\%$ interest compounded annually is $3$ years.