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03 Jan 2016, 12:17
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B
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72% (01:50) correct
28%
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wrong
based on 261
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If $ 5,000 is invested in an account that earns 8% interest compounded semi-annually, then the interest earned after one year would be how much greater than if the $ 5,000 had been invested at 8% simple yearly interest?
A. $ 4
B. $ 8
C. $ 12
D. $ 16
E. $ 432
A. $ 4
B. $ 8
C. $ 12
D. $ 16
E. $ 432
Praveengeol
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06 Jan 2016, 11:39
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Bunuel
ANS B
Solution
Amount (CI) = P+(1+r/n)^nt = 5000+(1+0.08/2)^2= 5408
Amount (SI) = P+PTR/100 = 5000+(5000*1*8/100)=5400
Difference = 5408-5400=8 $
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17 Jan 2020, 21:59
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Well to make it less calculation intensive we can think in this way.
Simple interest earned after one year for 8% = 5000*8/100 =400 $
Now for CI compounded semi annually interest is 4% for six month and 4% for another six month..
For 1st Six month it will be same as Simple interest earned for 4% = 5000*4/100=200$
for next six month = interest earned on interest will be only extra which makes its CI .
Hence interest earned on next six month = 200+ 4% of 200 = 200+ 4/100*200=200+8 = 208$
So total interest at end of 1 year in CI = 200+208 = 408 $
So only 8 $ difference between CI and SI.
I would suggest to get yourself acquainted with Interest earned on Interest using basic SI approach rather than CI formula. Most of the time it comes handy
Simple interest earned after one year for 8% = 5000*8/100 =400 $
Now for CI compounded semi annually interest is 4% for six month and 4% for another six month..
For 1st Six month it will be same as Simple interest earned for 4% = 5000*4/100=200$
for next six month = interest earned on interest will be only extra which makes its CI .
Hence interest earned on next six month = 200+ 4% of 200 = 200+ 4/100*200=200+8 = 208$
So total interest at end of 1 year in CI = 200+208 = 408 $
So only 8 $ difference between CI and SI.
I would suggest to get yourself acquainted with Interest earned on Interest using basic SI approach rather than CI formula. Most of the time it comes handy
