Question

₹6000 amounts to ₹7526.40 to for 2 years at a certain rate of interest compounded anually. find the rate of interest

Answer 1

Given:-

• Principal = ₹6000
• Amount = ₹7526.40
• Time = 2 years

To Find:-

• Rate of Interest

Formula Used:-

$\bf{Amount = Principal × {(1+\frac{Rate}{100})}^{time}}$

Solution:-

Let the rate of interest be x%

According to given conditions;

$\bf{ 7526.40= 6000 × {(1+\frac{x}{100})}^{2}}$

$\bf{ \implies 7526.40 ÷ 6000 = {(1+\frac{x}{100})}^{2}}$

$\bf{\implies 1.2544 = {(1+\frac{x}{100})}^{2}}$

$\bf{\implies \sqrt{1.2544} = (1+\frac{x}{100})}$

$\bf{\implies \sqrt{1.12 × 1.12} = (1+\frac{x}{100})}$

$\bf{\implies 1.12 = (1+\frac{x}{100})}$

$\bf{\implies 1.12 - 1 = \frac{x}{100}}$

$\bf{\implies 0.12 × 100 = x}$

$\huge{\tt{\therefore x = 12\%}}$

$\boxed{\pink{\therefore x = Rate = 12\%}}$