Harikiran purchased a house for Rs. 15000 and paid Rs. 5000 at once. Rest money he promised to pay in annual installments of Rs. 1000 with 10% per annum interest. How much money is to be paid by him in total?
Harikiran purchased a house for Rs. 15000 and paid Rs. 5000 at once. Rest money he promised to pay in annual installments of Rs. 1000 with 10% per annum interest. How much money is to be paid by him in total?
The correct option is C Rs. 20500
It will take 10 years for Harikiran to pay off Rs. 10000 in 10 yearly installments.
∵ He pays 10% annual interest on interest on the remaining amount
∴ Money given at the end of first year
= 1000 + 10000×10100 = Rs. 2000
Money given at the end of second year = 1000 + interest of (10000 - 1000) with interest rate 10% per annum
= 1000 + 9000×10100 = Rs. 1900
Money paid at the end 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
=102[2(2000)+(10−1)(−100)]=Rs.15500
Therefore, total money given by Harikiran
= 5000 + 15500 = Rs. 20500.
Rs. 20500
It will take 10 years for Harikiran to pay off Rs. 10000 in 10 yearly installments.
∵ He pays 10% annual interest on interest on the remaining amount
∴ Money given at the end of first year
= 1000 + 10000×10100 = Rs. 2000
Money given at the end of second year = 1000 + interest of (10000 - 1000) with interest rate 10% per annum
= 1000 + 9000×10100 = Rs. 1900
Money paid at the end 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
=102[2(2000)+(10−1)(−100)]=Rs.15500
Therefore, total money given by Harikiran
= 5000 + 15500 = Rs. 20500.
