Question

At what rate per cent of compound interest will a sum of ₹2,000 amount to ₹4,394 in 3 years?

• A. 25
• B. 20
• C. 30
• D. 35

Answer 1

Answer:

C. 30

The required rate of compound interest is 30% per annum.

1. Identify Given Values

• Principal ($P$) = ₹2,000

• Amount ($A$) = ₹4,394

• Time ($n$) = 3 years

• Rate ($R$) = ?

2. Apply Compound Interest Formula

The standard formula for the total amount under compound interest is:
$A = P \left(1 + \frac{R}{100}\right)^n$

Substitute the given values into the formula:
$4,394 = 2,000 \left(1 + \frac{R}{100}\right)^3$

3. Simplify the Ratio

Divide both sides by 2,000:
$\frac{4,394}{2,000} = \left(1 + \frac{R}{100}\right)^3$

Reduce the fraction to its simplest form by dividing the numerator and denominator by 2:
$\frac{2,197}{1,000} = \left(1 + \frac{R}{100}\right)^3$

4. Take the Cube Root

Recognize the perfect cubes on the left side ($2,197 = 13^3$ and $1,000 = 10^3$):
$\left(\frac{13}{10}\right)^3 = \left(1 + \frac{R}{100}\right)^3$

Take the cube root of both sides:
$\frac{13}{10} = 1 + \frac{R}{100}$

5. Solve for R

Subtract 1 from both sides:
$\frac{R}{100} = \frac{13}{10} - 1$

$\frac{R}{100} = \frac{3}{10}$

Multiply by 100:
$R = \frac{3}{10} \times 100 = 30\%$