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Jairam purchased a house in Rs. $15000$ and paid Rs. $5000$ at once. Rest money he promised to pay in annual installment of Rs. $1000$ with $10\%$ per annum interest. How much money is to be paid by Jairam $\mathrm{Rs.}$ ...................
$21555$
$20475$
$ 20500$
$ 20700$
Solution
(c) It will take $10$ years for Jairam to pay off Rs. $10000$ in $10$ yearly installments.
He pays $10\%$ annual interest on remaining amount
$\therefore $ Money given in first year
$ = 1000 + \frac{{10000 \times 10}}{{100}} = {\rm{Rs}}.2000$
Money given in second year $= 1000 +$ interest of$ (10000 -1000)$ with interest rate $10\%$ per annum $ = 1000 + \frac{{9000 \times 10}}{{100}} = {\rm{Rs}}.\,1900$
Money paid in third year = Rs. $1800$ etc.
So money given by Jairam in $10$ years will be Rs. $2000$, Rs. $1900$, Rs. $1800$, Rs. $1700$,….,
which is in arithmetic progression, whose first term $a = 2000$and $d = – 100$
Total money given in $10$ years = sum of $10$ terms of arithmetic progression
$ = \frac{{10}}{2}[2(2000) + (10 – 1)( – 100)]$= Rs. $15500$
Therefore, total money given by Jairam
$ = 5000 + 15500 = {\rm{Rs}}{\rm{. }}\,{\rm{20500}}{\rm{.}}$
