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If $ 5,000 is invested in an account that earns 8% interest compounded

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Math Expert
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If $ 5,000 is invested in an account that earns 8% interest compounded  [#permalink]

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New post 03 Jan 2016, 11:17
00:00
A
B
C
D
E

Difficulty:

  45% (medium)

Question Stats:

70% (01:54) correct 30% (02:03) wrong based on 104 sessions

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Joined: 02 Jun 2015
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Location: United States
Concentration: Strategy, Human Resources
WE: Engineering (Manufacturing)
Re: If $ 5,000 is invested in an account that earns 8% interest compounded  [#permalink]

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New post 06 Jan 2016, 10:39
Bunuel wrote:
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


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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If $ 5,000 is invested in an account that earns 8% interest compounded  [#permalink]

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New post 17 Jan 2020, 20:59
1
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
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If $ 5,000 is invested in an account that earns 8% interest compounded   [#permalink] 17 Jan 2020, 20:59
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