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# A man invests Rs 5000 for 3 years at 50% per annum compound

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A man invests Rs 5000 for 3 years at 50% per annum compound [#permalink]  09 Mar 2008, 10:00
A man invests Rs 5000 for 3 years at 50% per annum compound interest reckoned yearly.Income tax at the rate of 20% on the interest earned is deducted at the end of each year.Find the amount at the end of the third year.
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Re: Compound Interest [#permalink]  09 Mar 2008, 16:44
Total Amount at End of First Year = 5000*(1 + 50/100) = 5000*151/100 = 7550
Interest Earned on First Year = 7550 - 5000 = 2550
Income Tax = 2550*20/100 = 510
Total Amount to Be Invested For Second Year = 7550 - 510 = 7040
Now Total Amount at end of Second Year = 7040(1+50/100) = 10630.4
Interest Earner = 10630.4 - 7040 = 3590.4
Income Tax = 3590.4 *20/100 = 718.08
Total Amount to be invested for Third (Final Year) = 10630.4 - 718.8 = 9912.32

Now repeat for 3rd year and you have the answer.
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Re: Compound Interest [#permalink]  09 Mar 2008, 18:35
Vemuri wrote:
A man invests Rs 5000 for 3 years at 50% per annum compound interest reckoned yearly.Income tax at the rate of 20% on the interest earned is deducted at the end of each year.Find the amount at the end of the third year.

Is it a GMAT question to be solved within 2 minutes? It needs sheer brute force to solve, or one needs to define the generic formula for this case. Answer by Abhijit is the only approach I can think of!
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Re: Compound Interest [#permalink]  10 Mar 2008, 18:05
abhijit_sen wrote:
Total Amount at End of First Year = 5000*(1 + 50/100) = 5000*151/100 = 7550
Interest Earned on First Year = 7550 - 5000 = 2550
Income Tax = 2550*20/100 = 510
Total Amount to Be Invested For Second Year = 7550 - 510 = 7040
Now Total Amount at end of Second Year = 7040(1+50/100) = 10630.4
Interest Earner = 10630.4 - 7040 = 3590.4
Income Tax = 3590.4 *20/100 = 718.08
Total Amount to be invested for Third (Final Year) = 10630.4 - 718.8 = 9912.32

Now repeat for 3rd year and you have the answer.

Total Amount at End of First Year = 5000*(1 + 50/100) = 5000*150/100 = 7500
Interest Earned on First Year = 7500 - 5000 = 2500
Income Tax = 2500*20/100 = 500
Total Amount to Be Invested For Second Year = 7500 - 500 = 7000
Now Total Amount at end of Second Year = 7000(1+50/100) = 10500
Interest Earner = 10500 - 7000 = 3500
Income Tax = 3500 *20/100 = 700
Total Amount to be invested for Third (Final Year) = 10500 - 700 = 9800

It is pretty straight forward as the numbers are all whole numbers
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Re: Compound Interest   [#permalink] 10 Mar 2008, 18:05
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