Question

What annual installment will discharge a debt of 1815 due in 3 years at \[10%\] simple interest?
    a). 500
    b). 520
    c). 550
   d). 580

Answer 1

Hint: We will assume the monthly installment be Rs.x, then we will use formula of \[\text{simple}\ \text{interest} =\dfrac{P\times R\times T}{100}\] where P = Principal, R = Rate of interest and T = Time, to find the value of x.

Complete step-by-step solution -
It is given in the question that the due amount is Rs.1815 which we have to pay in 3 years also the interest rate is 10%. Let us assume that the monthly installment is Rs.x. We will use the formula of simple interest to solve the problem. We know that, \[simple\text{ }interest=\dfrac{P\times R\times T}{100}\] where P = Principal, R = Rate of interest and T = Time.
So, for the first year, we calculate installment + interest. \[Installment=x\] and \[interest=\dfrac{P\times R\times T}{100}=\dfrac{x\times 10\times 1}{100}=\dfrac{x}{10}\], therefore \[installment\text{ }+\text{ }interest\text{ }=x+\dfrac{x}{10}=\dfrac{11x}{10}\].
Similarly, installment for 2nd year will be $x+\dfrac{x\times 10\times 2}{100}=x+\dfrac{x}{5}=\dfrac{6x}{5}$.
For the third year installment will be x as we have to pay all in third year. We know that total amount is equal to Rs.1815, which means $\dfrac{11x}{10}+\dfrac{6x}{5}+x=1815$.
Taking LCM as 10 in LHS, we get $\dfrac{11x+12x+10x}{10}=1815$, simplifying further, we get $11x+12x+10x=18150$, on summing the LHS, we get $33x=18150$, Therefore, $x=\dfrac{18150}{33}=550$.
Thus, the monthly installment will be Rs 550 and therefore option c) is the correct answer.

Note: Generally students directly find the interest on Rs 1815 using formula of simple interest and then add with principal amount, then divide it with time period but this is not correct because man is also repaying in all three years and the final amount deposited will be less as the amount of interest is less that interest on Rs 1815 for three complete years.