Question

What annual instalment will discharge a debt of Rs.2710 due in 4 years at 7% simple interest?
A. Rs.1000.
B. Rs.613.
C. Rs.225.
D. Rs.150.

Answer 1

Hint: Let Rs. x be the annual instalment. Now, x accumulates an interest of 7% every year. In this way find the value of x deposited in the 4 years and solve the question.

Complete step by step answer:
We know that,
First year instalment = $x + \dfrac{{x \times {\text{interest}} \times {\text{time}}}}{{100}}$
Here time = 1 year.
So,
$1^{st}$ year instalment = $x + \dfrac{{x \times 7 \times 1}}{{100}} = \dfrac{{107x}}{{100}}$
$1^{st}$ year instalment = 1.07x.
Similarly,
$2^{nd}$ year instalment = $x + \dfrac{{x \times 7 \times 2}}{{100}} = \dfrac{{114x}}{{100}}$
$2^{nd}$ year instalment = 1.14x.
$3^{rd}$ year instalment = $x + \dfrac{{x \times 7 \times 3}}{{100}} = \dfrac{{121x}}{{100}}$
$3^{rd}$ year instalment = 1.21x.
$4^{th}$ year instalment = x.
Now, we have to find the annual instalment that will discharge a debt of Rs.2710.
So,
Adding all year’s instalment,
\[ \Rightarrow 1.07x + 1.14x + 1.21x + x = 2710\]
\[ \Rightarrow 4.42x = 2710\]
\[ \Rightarrow x = \dfrac{{2710}}{{4.42}}\]
\[ \Rightarrow x = 613.12\]
We can write this as: x = Rs.613.
Hence, we can say that the annual instalment that will discharge a debt of Rs.2710 is Rs.613.

So, the correct answer is “Option B”.

Note: Whenever we ask such types of questions, we have to remember some basic steps. First, we have to find out all the given details. Then we will assume that x be that annual instalment. After that, we will find the amount of installments for every year and then by adding those amounts and equating it with the debt, we will get the value of x and through this, we will get the required answer.