Question
One can purchase a flat from a house building society for Rs. 55000 cash or on the terms that he should pay Rs. 4275 as cash down payment and get the rest in three equal installments. The society charges interest at the rate of 16% per annum compounded half-yearly. If the flat is purchased under installment plan, find the value of each installment ?
Answer: Option C
Total cost of the flat = Rs. 55000
Down payment = Rs. 4275
Balance = Rs. (55000 - 4275) = Rs. 50725
Rate of interest = 8% per half year
Let the value of each instalment be Rs. x
P.W. of Rs. x due 6 months hence + P.W. of Rs. x due 1 year hence + P.W. of Rs. x due $$1\frac{1}{2}$$ years hence = 50725
$$ \Rightarrow \frac{x}{{\left( {1 + \frac{8}{{100}}} \right)}} + $$ $$\frac{x}{{{{\left( {1 + \frac{8}{{100}}} \right)}^2}}} + $$ $$\frac{x}{{{{\left( {1 + \frac{8}{{100}}} \right)}^3}}} = $$ $$50725$$
$$\eqalign{
& \Rightarrow \frac{{25x}}{{27}} + \frac{{625x}}{{729}} + \frac{{15625x}}{{19683}} = 50725 \cr
& \Rightarrow \frac{{50725x}}{{19683}} = 50725 \cr
& \Rightarrow x = \left( {\frac{{50725 \times 19683}}{{50725}}} \right) = 19683 \cr} $$
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Total cost of the flat = Rs. 55000
Down payment = Rs. 4275
Balance = Rs. (55000 - 4275) = Rs. 50725
Rate of interest = 8% per half year
Let the value of each instalment be Rs. x
P.W. of Rs. x due 6 months hence + P.W. of Rs. x due 1 year hence + P.W. of Rs. x due $$1\frac{1}{2}$$ years hence = 50725
$$ \Rightarrow \frac{x}{{\left( {1 + \frac{8}{{100}}} \right)}} + $$ $$\frac{x}{{{{\left( {1 + \frac{8}{{100}}} \right)}^2}}} + $$ $$\frac{x}{{{{\left( {1 + \frac{8}{{100}}} \right)}^3}}} = $$ $$50725$$
$$\eqalign{
& \Rightarrow \frac{{25x}}{{27}} + \frac{{625x}}{{729}} + \frac{{15625x}}{{19683}} = 50725 \cr
& \Rightarrow \frac{{50725x}}{{19683}} = 50725 \cr
& \Rightarrow x = \left( {\frac{{50725 \times 19683}}{{50725}}} \right) = 19683 \cr} $$
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