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I found this problem while helping my nephew with his "O" level mathematics. My solution doesn't match the answer. Can anybody point out the error in my procedure?

"A woman buys a house valued at \$18000. She pays 30% of its value immediately, \$6000 eighteen months later and the remainder after a further eighteen months. Simple interest is charged at 4.5% per annum. Find how much she pays altogether?"

My solution 18000+(12600*0.045*1.5)+(6600*0.045*1.5) = 19296 doesnt' match the answer. The answer is given \$19350

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Perhaps the answer given in the book is wrong. The book answer would be correct for a problem in which the payments were $5000, $6000, and $7000 plus accumulated interest instead of $5400, $6000 and $6600 plus accumulated interest. So one explanation would be that the $5000 initial payment was changed to 30% at some time after the answers were computed for the original version, and the answer did not get updated. –  Dilip Sarwate Sep 20 '12 at 13:09
    
Thank you sir, I am sending an email to the publication of the book :) –  Sabirul Mostofa Sep 20 '12 at 13:56

2 Answers 2

It appears that the answer in the book is incorrect. As Dilip Sarwate pointed out in the comments:

Perhaps the answer given in the book is wrong. The book answer would be correct for a problem in which the payments were $5000,6000$, and $7000$ plus accumulated interest instead of $5400, 6000$ and $6600$ plus accumulated interest. So one explanation would be that the $5000$ initial payment was changed to $30\%$ at some time after the answers were computed for the original version, and the answer did not get updated.

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Yes the answer calculated by you is correct , a reverse calculation can prove it true.

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