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02 Aug 2018, 00:21
00:00

Difficulty:

35% (medium)

Question Stats:

80% (02:28) correct 20% (01:52) wrong based on 25 sessions

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If $1000 is placed into account X, yielding 10% interest compounded annually and$1000 is placed into account Y using 10% simple annual interest, how much more will be in account X than in account Y at the end of 5 years?

A. $0 B.$100
C. $110.51 D.$133.31
E. $146.41 _________________ Director Joined: 30 Jan 2015 Posts: 525 Location: India Concentration: Operations, Marketing GPA: 3.5 Re: If$1000 is placed into account X, yielding 10% interest compounded an  [#permalink]

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02 Aug 2018, 02:52
S.I = P*T*R / 100 = 1000 * 5 * 0.1 = 500
C.I = P*( 1 + R/100 )^nt - P = 1000 * ( 1 + 0.1 )^5 - 1000 = 1610.51 - 1000 = 610.51

C.I - S.I = 610.51 - 500 = 110.51

Hence, C.
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Re: If $1000 is placed into account X, yielding 10% interest compounded an [#permalink] ### Show Tags 02 Aug 2018, 03:30 Bunuel wrote: If$1000 is placed into account X, yielding 10% interest compounded annually and $1000 is placed into account Y using 10% simple annual interest, how much more will be in account X than in account Y at the end of 5 years? A.$0
B. $100 C.$110.51
D. $133.31 E.$146.41

A simple interest of 10% every year will increase the principal by 0.1(x will become 1.1) in a year.
The principal will increase by the same time every year and becomes $$x + 5(0.1x) = 1.5x$$ in 5 years.

On the contrary, the compound interest will be $$x*(1.1)^5 = x(1.331*1.21) = 1.61051x$$

The difference between the amount in account X and account Y is $$1.61051x - 1.5x = 0.11051x$$

Therefore, since the amount placed is $1000, there is 0.11051*1000 =$110.51(Option C) more in account X.
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