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The difference in compound interest earned on a deposit (compounded an

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The difference in compound interest earned on a deposit (compounded an  [#permalink]

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New post Updated on: 08 Dec 2014, 04:49
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The difference in compound interest earned on a deposit (compounded annually) in year 1 and year 2 is $ 40. Had the interest rate been three times its present value, the difference would have been how much?

A) 40/3
B) 40
C) 120
D) 360
E) 420

Originally posted by desaichinmay22 on 08 Dec 2014, 04:32.
Last edited by Bunuel on 08 Dec 2014, 04:49, edited 1 time in total.
Edited the question.
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Re: The difference in compound interest earned on a deposit (compounded an  [#permalink]

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New post 08 Dec 2014, 04:53
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desaichinmay22 wrote:
The difference in compound interest earned on a deposit (compounded annually) in year 1 and year 2 is $ 40. Had the interest rate been three times its present value, the difference would have been how much?

A) 40/3
B) 40
C) 120
D) 360
E) 420


CASE 1:
Deposit = $x;
Rate of increase = r.

Interest yearned in 1 year = xr. Deposit in 1 year = x + xr.
Interest yearned in 2 year = (x + xr)r.
The difference = (x + xr)r - xr = xr^2 = 40.

CASE 2:
Deposit = $x;
Rate of increase = 3r.

Interest yearned in 1 year = x(3r). Deposit in 1 year = x + 3xr.
Interest yearned in 2 year = (x + 3xr)3r.
The difference = (x + 3xr)3r - 3xr = 9xr^2. Since from CASE 1 we know that xr^2 = 40, then 9xr^2 = 9*40 = 360.

Answer: D.

Hope it's clear.
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Re: The difference in compound interest earned on a deposit (compounded an  [#permalink]

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New post 08 Dec 2014, 04:54
Let Deposit be P, Let rate of interest be R (in decimal)
Compound interest earned in 1st year = P(1+R)^1 - P = PR [CI = P*(1+R)^n]
Compound interest earned in 2nd year = P(1+R)^2 - PR - P [CI for 2 years - Interest in 1st year - Principal] = P + 2PR + PR^2 - PR - P = PR + PR^2
Difference in compound interest earned in 1st and 2nd year =
PR + PR^2 - (PR)
= PR^2 = 40

If rate of interest is 3R then
(following similar procedure) Difference in Compound interest would be = P*(3R)^2 = 9PR^2

So, Difference will be 9 * 40 = 360
So, Answer will be D

Hope it helps!

desaichinmay22 wrote:
The difference in compound interest earned on a deposit (compounded annually) in year 1 and year 2 is $ 40. Had the interest rate been three times its present value, the difference would have been how much?

A)40/3
B)40
C)120
D)360
E)420

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Re: The difference in compound interest earned on a deposit (compounded an  [#permalink]

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Re: The difference in compound interest earned on a deposit (compounded an &nbs [#permalink] 02 Mar 2018, 21:33
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