Question

What annual installment will discharge a debt of Rs.1092 in due in 3 years at 12% simple interest?
$
  (a){\text{ 1485}}{\text{.12}} \\
  (b){\text{ 1480}}{\text{.12}} \\
  (c){\text{ 442}} \\
  (d){\text{ none of these}} \\
 $

Answer 1

Hint – In this question use the concept that the ultimate amount that is to be paid by 3 years to clear off the debt will be the addition of the principal amount that is 1092 and the simple interest computed for 3 years. So let annual installments per year be some x rupees so for 3 years this installments will amount to 3x rupees. Thus use the direct formula for simple interest that is $SI = \dfrac{{P \times R \times T}}{{100}}$. This will help getting the answer.

Complete step-by-step answer:
As we know in simple interest, the interest is not added in the principle amount during the years.
So the amount (A) has to be paid = 1092 as the principal amount + simple interest of the three years.
Let the annual installments per year be X Rs.
So we had to pay 3X annual installments in three years.
Therefore,
1092 as the principal amount + simple interest of the three years = 3X.......... (1)
Now the rate of interest is given = 12%
As we know simple interest is calculated as (S.I) = $\dfrac{{p \times r \times t}}{{100}}$
Where p = principle amount, r = rate of interest and t = time in years.
So during the first year simple interest is $S.{I_1} = \dfrac{{1092 \times 12 \times 1}}{{100}} = 131.04$ Rs.
Now in second year the principle remains = (1092 – X)
So during second year simple interest is $S.{I_2} = \dfrac{{\left( {1092 - X} \right) \times 12 \times 1}}{{100}} = 131.04 - 0.12X$ Rs.
Now in final year i.e. in third year the principle remains = (1092 – 2X)
So during third year simple interest is $S.{I_2} = \dfrac{{\left( {1092 - 2X} \right) \times 12 \times 1}}{{100}} = 131.04 - 0.24X$ Rs.
Now from equation (1) we have,
$ \Rightarrow 1092 + 131.04 + 131.04 - 0.12X + 131.04 - 0.24X = 3X$
Now simplify this equation we have,
\[ \Rightarrow 1092 + 3\left( {131.04} \right) - 0.36X = 3X\]
$ \Rightarrow 3.36X = 1092 + 393.12 = 1485.12$
$ \Rightarrow X = \dfrac{{1485.12}}{{3.36}} = 442$ Rs.
So this is the required annual installment we have to pay that will discharge a debt of Rs.1092.
Hence option (C) is the required answer.

Note – There is a bit of confusion regarding the difference between simple interest and compound interest. A simple interest is based upon the principal amount of a loan, whereas a compound interest is the principal amount and in addition to the interest that accumulates over it on every period of loan duration tenure.