• # question_answer 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 [UPSEAT 1999] A) Rs. 21555 B) Rs. 20475 C) Rs. 20500 D) Rs. 20700

It will take 10 years for Jairam to pay off  Rs. 10000 in 10 yearly installments. $\because$ He pays 10% annual interest on remaining amount $\therefore$  Money given in first year $=1000+\frac{10000\times 10}{100}=\text{Rs}.2000$ Money given in second year = 1000 + interest of  (10000 - 1000) with interest rate 10% per annum $=1000+\frac{9000\times 10}{100}=\text{Rs}.\,1900$ 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 $=5000+15500=\text{Rs}\text{. }\,\text{20500}\text{.}$