A sum of money becomes ₹20070 after 3 year and ₹30105 after 6 years on compound interest. The sum will be

13380

The correct answer is Option (1) → 13380

We are given:

• Amount after 3 years: $A_3 = 20070$
• Amount after 6 years: $A_6 = 30105$

The compound interest formula:

$A = P(1 + r)^t$

Step 1: Express $A_6$​ in terms of $A_3$​

$A_6 = A_3 \cdot (1 + r)^3$

$30105 = 20070 \cdot (1 + r)^3$

$(1 + r)^3 = \frac{30105}{20070} \approx 1.5$

$1 + r = \sqrt[3]{1.5} \approx 1.1447$

Step 2: Find the principal P

$A_3 = P (1 + r)^3 ⇒20070 = P \cdot 1.1447^3$

But $1.1447^3 \approx 1.5$, so:

$20070 = P \cdot 1.5 ⇒P = \frac{20070}{1.5} \approx 13380$