Question : What annual instalment(in INR approx.) will discharge a debt of INR 9,429 due in three years at 12.25% simple interest per annum? [Note: Instalments will be paid at the end of Year 1, Year 2 and Year 3.]
Option 1: 2,840
Option 2: 2,800
Option 3: 2,700
Option 4: 2,760
Correct Answer: 2,800
Solution : Let the required annual instalment be INR $x$. The calculated equation for the first year is equal to the sum of instalment and interest of the remaining two years as follows: ⇒ [$x + \frac{x × 12.5 × 2}{100}$] The calculated equation for the second year is equal to the sum of instalment and interest of the remaining year is as follows: ⇒ [$x + \frac{x × 12.5 × 1}{100}$] The calculated equation for the third year is equal to the instalment only as no other year remains is $x$. Now, $[x + \frac{\text{$x$ × 12.5 × 2}}{100}] + [x + \frac{\text{$x$ × 12.5 × 1}}{100}]$$+ x = 9429$ ⇒ $[3x + \frac{\text{$25x$}}{100} + \frac{\text{$12.5x$}}{100}] = 9429$ ⇒ $\frac{\text{$337.5x$}}{100} = 9429$ ⇒ $x = 2793.78 \approx 2800$ Hence, the correct answer is INR 2,800.
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