Question

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

• A. Rs. 21555
• B. Rs. 20475
• C. Rs. 20500
• D. Rs. 20700

Answer 1

The correct option is C

Rs. 20500

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
$=1000+\frac{10000\times 10}{100}=Rs.2000$
Money given in second year = 1000 + interest of (10000 – 1000) with interest rate 10% per annum $=1000+\frac{9000\times 10}{100}=Rs.1900$
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
$=\frac{10}{2}\left[2\right(2000)+(10-1\left)\right(-100\left)\right]=Rs.15500$
Therefore, total money given by Jairam
= 5000 + 15500 = Rs.20500.