What annual instalment will discharge a debt of ₹ 4,600 due in 4 years at 10% simple interest?

1. ₹ 1,000

2. ₹ 1,150

3. ₹ 1,500

4. ₹ 1,610

Let annual installment be ₹ x.

Annual installment 1 (Paid at the end of 1st year) : This installment will earn interest for 3 years.

$\Rightarrow x + x \times \dfrac{10}{100} \times 3 \\[1em] \Rightarrow x + \dfrac{3x}{10} \\[1em] \Rightarrow \dfrac{13x}{10} \\[1em] \Rightarrow 1.3x$

Annual installment 2 (Paid at the end of 2nd year) : This installment will earn interest for 2 years.

$\Rightarrow x + x \times \dfrac{10}{100} \times 2 \\[1em] \Rightarrow x + \dfrac{2x}{10} \\[1em] \Rightarrow \dfrac{12x}{10} \\[1em] \Rightarrow 1.2x$

Annual installment 3 (Paid at the end of 3rd year) : This installment will earn interest for 1 year.

$\Rightarrow x + x \times \dfrac{10}{100} \times 1 \\[1em] \Rightarrow x + \dfrac{x}{10} \\[1em] \Rightarrow \dfrac{11x}{10} \\[1em] \Rightarrow 1.1x$

Annual installment 4 (Paid at the end of 4th year) : This installment will not earn any interest.

⇒ x

The sum of these values must be equal to debt value of ₹ 4,600.

⇒ 1.3x + 1.2x + 1.1x + x = 4,600

⇒ 4.6x = 4,600

⇒ x = $\dfrac{4,600}{4.6}$

⇒ x = ₹ 1,000.

Hence, Option 1 is correct option.