Simple interest of an amount for a period of 12 years is Rs.2400. If the amount is tripled after 3 years then what will be the interest after 12 years?

Given:

Simple interest for 12 years = ₹2400

Time (t) = 12 years

After 3 years, amount is tripled

Formula used:

Simple Interest (SI) = \(P × \frac{r × t}{100}\)

Calculation:

Let the original principal amount be P

SI for 12 years = \(P × \frac{r × 12}{100}\)

⇒ ₹2400 = \(P × \frac{r × 12}{100}\)

⇒ \(\frac{PR}{100}\) = 200   ............(1)

SI for first 3 years = \(P × \frac{r × 3}{100}\)

After 3 years, the principal amount is tripled, so new principal amount = 3P

SI for the remaining 9 years = \(3P × \frac{r × 9}{100}\)

Total SI = SI for first 3 years + SI for the remaining 9 years

⇒ SI = \(P × \frac{r × 3}{100}\) + \(3P × \frac{r × 9}{100}\)

⇒ SI = \(P × \frac{3r}{100}\) + \(3P × \frac{9r}{100}\)

⇒ SI = \(P × \frac{3r}{100}\) + \(27P × \frac{r}{100}\)

⇒ SI = \(\frac{30PR}{100}\)

⇒ SI = 30 × 200    (From eqn 1, \(\frac{PR}{100}\) = 200 )

⇒ SI = 6000

Therefore, the interest after 12 years is Rs 6000

∴ The correct answer is option (4).