Question

# Harikiran purchased a house in Rs. 15000 and paid Rs. 5000 at once. Rest money he promised to pay in annual instalment of Rs. 1000 with 10% per annum interest. How much money is to be paid by him

A

Rs. 21555

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B

Rs. 20475

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C

Rs. 20500

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D

Rs. 20700

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Solution

## 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 remaining amount ∴ Money given in first year = 1000 + 10000×10100 = Rs. 2000 Money given in second year = 1000 + interest of (10000 - 1000) with interest rate 10% per annum = 1000 + 9000×10100 = 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 = 102[2(2000) + (10 - 1)(-100)] = Rs. 15500 Therefore, total money given by harikiran = 5000 + 15500 = Rs. 20500.

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