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Interest

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Manager
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Interest [#permalink] New post 28 Aug 2009, 05:55
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If Jaques deposists $1000 in a savings account at 10% simple annual interest, how much more will he earn than if he had deposited it in an account that pays 8 percent annueal interest compounded semiannually?

a) $20.00
b) $19.60
c) $18.40
d) $18.00
e) $17.40
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Re: Interest [#permalink] New post 28 Aug 2009, 06:54
\(1000(1+\frac{0.08}{2})^2-1000(1+0.1)\)
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Re: Interest [#permalink] New post 28 Aug 2009, 08:26
With Deposit A he will earn 10% on 1,000 for 1 year = $100

With Deposit B he will earn 8/2 (Semi) 4% on $1,000 for 6 months = $40
And will earn 4% on $1,040 ($ are compounded) for 6 months = $41.60

$100.00 - $81.60 = $18.40
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Re: Interest [#permalink] New post 28 Aug 2009, 08:30
I have always problems with interests rates

Any suggestion to get better at it?

Thanks a lot
Manager
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Re: Interest [#permalink] New post 28 Aug 2009, 08:51
It really depends on if you like to work it through step by step or an equation.

I prefer doing it the same way as Casper with the Present Value equation of \(FV=PV(1+\frac{I}{n})^n\)

Where i = Interest rate and N = # of periods compounded an PV = Initial Deposit

Once you get down the compounding these questions should become easy
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Re: Interest [#permalink] New post 28 Aug 2009, 12:39
S.I = P*R*T/100 = 1000*10*1/100 = 100
Total amount = 1000 + 100 = 1100

C.I. = P(1+R/n)^Tn

= 1000*(1 + 8/200)^2 = 1000*(1.04)^2 = 1081.6

Remember, C.I formula gives total amount while S I formula gives only the interest.

Difference = 1100 - 1081.6 = 18.4
Re: Interest   [#permalink] 28 Aug 2009, 12:39
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