Question
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 ?
Answer: Option B
Let the value of each instalment be Rs. x
Then, (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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Let the value of each instalment be Rs. x
Then, (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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