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 instalments. The society charges interest at the rate of 16% per annum compounded half - yearly. If the flat is purchased under instalment plan, find the value of each instalment = ?

1Rs. 18756
2Rs. 19292
3Rs. 19683
4Rs. 20285

Answer:- 1

Explanation:-

Solution:

Total cost of the flat = Rs. 55000.
Down payment = Rs. 4275
Balance = Rs. (55000 - 4275) = Rs. 50725
Rate of interest = 85 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 1¹/₂ years hence = 50725

\begin{aligned} \Rightarrow \frac{x}{(1 + \frac{8}{100})} + \frac{x}{{(1 + \frac{8}{100})}^{2}} + \frac{x}{{(1 + \frac{8}{100})}^{3}} = 50725 \\ \Rightarrow \frac{25 x}{27} + \frac{625 x}{729} + \frac{15625 x}{19683} = 50725 \\ \Rightarrow \frac{50725 x}{19683} = 50725 \\ \Rightarrow x = (\frac{50725 \times 19683}{507250}) = 19683 \end{aligned}

$\eqalign{ & \Rightarrow \frac{x}{{\left( {1 + \frac{8}{{100}}} \right)}} + \frac{x}{{{{\left( {1 + \frac{8}{{100}}} \right)}^2}}} + \frac{x}{{{{\left( {1 + \frac{8}{{100}}} \right)}^3}}} = 50725 \cr & \Rightarrow \frac{{25x}}{{27}} + \frac{{625x}}{{729}} + \frac{{15625x}}{{19683}} = 50725 \cr & \Rightarrow \frac{{50725x}}{{19683}} = 50725 \cr & \Rightarrow x = \left( {\frac{{50725 \times 19683}}{{507250}}} \right) = 19683 \cr}$