Under the Rural Housing Scheme, the Delhi Development Authority (DDA) allotted a house to Kamal Raj for Rs. 126100. This payment is to be made in three equal annual instalments. If the money is reckoned at 5% per annum compound interest, then how much is to be paid by Kamal Raj in each instalment ?
A. Rs. 45205
B. Rs. 46305
C. Rs. 47405
D. Rs. 48505
Answer: Option B
Solution(By Examveda Team)
Let the value of each instalment be Rs. xThen, (P.W. of Rs. x due 1 year hence) + (P.W. of Rs. x due 2 year hence) + (P.W. of Rs. x due 3 year hence) = 126100
$$\eqalign{ & \Rightarrow \frac{x}{{\left( {1 + \frac{5}{{100}}} \right)}} + \frac{x}{{{{\left( {1 + \frac{5}{{100}}} \right)}^2}}} + \frac{x}{{{{\left( {1 + \frac{5}{{100}}} \right)}^3}}} = 126100 \cr & \Rightarrow \frac{{20x}}{{21}} + \frac{{400x}}{{441}} + \frac{{8000x}}{{9261}} = 126100 \cr & \Rightarrow \frac{{8820x + 8400x + 8000x}}{{9261}} = 126100 \cr & \Rightarrow \frac{{25220x}}{{9261}} = 126100 \cr & \Rightarrow x = \left( {\frac{{126100 \times 9261}}{{25220}}} \right) \cr & \Rightarrow x = 46305 \cr} $$
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Since interest is 5% ,
Thus Interest to Principle Ratio = (21/20)
1st Year Installment of Principle ( after discounting) = (20*21*21) = 8820
2nd Year Installment of Principle ( after discounting)= ( 20*20*21) = 8400
3rd year Installment of Principle ( after discounting)= ( 20*20*20) = 8000
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Total Principle = 25220 unit
Here Installment including interest in each year =( 21*21*21)= 9261 unit
25220 unit = 126100
1 unit = (126100/25220) unit
Thus 9261 unit ( installment) = (126100/25220)*9261=( 5*9261)=46305
Answer: 46305