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$2000 is invested in a new savings account at r percent interest rate

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Bunuel
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$2000 is invested in a new savings account at r percent interest rate [#permalink] New post   13 Dec 2022, 10:15
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$2000 is invested in a new savings account at r percent interest rate compounded annually. If the amount in the account after 3 years is $3456, what is the total interest (in dollars) earned after 2 years of starting the account?

A. 360
B. 728
C. 747
D. 880
E. 920
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D
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karapucho
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$2000 is invested in a new savings account at r percent interest rate [#permalink] New post   16 Dec 2022, 15:06
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Amount 3456 - 2000 = 1456
logically divided by 3 years approximately 480 per year. ( the amount of savings is not big so the difference between earnings each year will not be big as well). The question what is the interest earned after 2 years?

A ) 360 - too small
B) 728 - too small
C) 747 - let's see ( 2000 + 747 = 2747, 3456 - 2747= 709$ ( for the last year and the difference is way too big between the interest earned previously in two years.

D) 880 - this amount looks perfect and easy to calculate.
2000 with the interest of 20% ( 400$) = 2400 ( first year)
2400 with same interest 20 % ( 440$) = 2 880 ( second year)
2880 + interest 20% ( 576$) = 3 456 ( third year)

E) 920 - too big.

I hope it was helpful.
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Re: $2000 is invested in a new savings account at r percent interest rate [#permalink] New post   16 Dec 2022, 15:56
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Bunuel wrote:
$2000 is invested in a new savings account at r percent interest rate compounded annually. If the amount in the account after 3 years is $3456, what is the total interest (in dollars) earned after 2 years of starting the account?

A. 360
B. 728
C. 747
D. 880
E. 920


Let interest be r
3456= 2000(1+r/100)^3

1728/1000 = (1+r/100)^3

or(1+r/100)= 12/10
or r= 20

Amount after 2 years = 2000(1.2)^2=2880 thus interest earned = 2880-2000 = 880 hence option D
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Re: $2000 is invested in a new savings account at r percent interest rate [#permalink] New post   16 Dec 2022, 18:19
$2000 is invested in a new savings account at r percent interest rate compounded annually. If the amount in the account after 3 years is $3456, what is the total interest (in dollars) earned after 2 years of starting the account?

A. 360
B. 728
C. 747
D. 880
E. 920


Given, 2000 (1+r)^3 = 3456
Solving, r = 0.2 = 20% p.a.

In two years, Amount = 2000 (1+r)^2 = 2880
Hence, interest earned after 2 years of staring the account = 2880 - 2000 = $ 880

IMO, the answer will be (D)
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Re: $2000 is invested in a new savings account at r percent interest rate [#permalink] New post   16 Dec 2022, 23:34
Given: $2000 is invested in a new savings account at r percent interest rate compounded annually.

Asked: If the amount in the account after 3 years is $3456, what is the total interest (in dollars) earned after 2 years of starting the account?

About after 3 years = $2000 (1+r)^3 = $3456
(1+r)^3 = 3456/2000 = 1.728
r = 20%

Total interest earned after 2 years of starting the account = $2000 {(1+r)^2 - 1} = $2000{1.2^2 - 1} = $2000(1.44 -1) = $2000*.44 = $880

IMO D
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Re: $2000 is invested in a new savings account at r percent interest rate [#permalink] New post   26 Mar 2024, 23:08
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Re: $2000 is invested in a new savings account at r percent interest rate [#permalink]
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