What annual installment will discharge a debt of Rs 4600 due in 4 years at 10% simple interest 1 point 1000 1030 1100 none of these?

Answer

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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.