Question

What annual installment will discharge a debt of INR 1092 due in 3 years at 12 % simple interest?
(a). INR 250
(b). INR 275
(c). INR 300
(d). INR 325

Answer 1

- Hint: The formula to calculate the simple interest for a principal amount P, at a rate of R % per annum for N years is given as $$SI={\displaystyle \frac{PNR}{100}}$$. Use this to calculate the annual installment in each year and equate it to the total debt of INR 1092.

Complete step-by-step answer: -

We know that the formula to calculate simple interest for a principal amount P, at a rate of R % per annum for N years is given as follows:
$$SI={\displaystyle \frac{PNR}{100}}$$
Let us assume that the annual installment is Rs. X for each year.
In the first year, we pay Rs. X, this amount will produce interest for the next two years. Hence, the total amount generated by the first installment is given as follows:
$$A_1=X+{\displaystyle \frac{X(2)(12)}{100}}$$
Simplifying, we have:
$$A_1=X+{\displaystyle \frac{6X}{25}}$$
$$A_1={\displaystyle \frac{25X+6X}{25}}$$
$$A_1={\displaystyle \frac{31X}{25}}...............(1)$$
In the second year, we pay Rs. X, this amount will produce interest for the next one year. Hence, the total amount generated by the second installment is given as follows:
$$A_2=X+{\displaystyle \frac{X(1)(12)}{100}}$$
Simplifying, we have:
$$A_2=X+{\displaystyle \frac{3X}{25}}$$
$$A_2={\displaystyle \frac{25X+3X}{25}}$$
$$A_2={\displaystyle \frac{28X}{25}}...............(2)$$
In the third year, we settle the installment by paying Rs. X, hence, we have:
$$A_3=X...............(3)$$
The total amount at the end of the third year should be equal to INR 1092. Hence, using equations (1), (2), and (3), we have:
$$A_1+A_2+A_3=1092$$
$${\displaystyle \frac{31X}{25}}+{\displaystyle \frac{28X}{25}}+X=1092$$
Multiplying both sides by 25, we have:
$$31X+28X+25X=1092\times 25$$
Simplifying we have:
$$84X=1092\times 25$$
Solving for X, we have:
$$X={\displaystyle \frac{1092\times 25}{84}}$$
$$X=325$$
Hence, the correct answer is option (d).

Note: Note that you should not apply the formula considering the amount INR 1092 as the principal amount. The concept is wrong. Assume the installment as X and then proceed.