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$2,000 is deposited in a savings account that pays 6% annual interest

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$2,000 is deposited in a savings account that pays 6% annual interest  [#permalink]

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New post 26 Jan 2016, 01:49
00:00
A
B
C
D
E

Difficulty:

  25% (medium)

Question Stats:

71% (01:13) correct 29% (01:26) wrong based on 134 sessions

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$2,000 is deposited in a savings account that pays 6% annual interest compounded semiannually. To the nearest dollar, how much is in the account at the end of the year?

A. $2,060
B. $2,120
C. $2,122
D. $2,247
E. $2,258

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Re: $2,000 is deposited in a savings account that pays 6% annual interest  [#permalink]

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New post 26 Jan 2016, 03:23
1
Principal = 2000 $
Annual interest rate = 6%
Semiannually means twice a year
Number of compounding periods = 2
So 6% is split into two
3 % halfway through the year
3% at the end of the year

Interest for first half of year= 2000 * (3/100) = 60 $
Interest for second half of year = 2060 * (3/100) = 61.8 $
Total interest = 121.8$
Total amount in account at the end of year = 2121.8 $

Answer C

Alternatively , we can use estimation here
To simplify if we assume that compounding was done only once a year , then interest earnerd will be
= 2000 * (6/100)
=120 $
So , we can immediately eliminate options A and B.
The interest earned in option D and E are approximately around 247 and 258 $ ,which will approximately be equal to
effective annual interest rate of 12.5 %. Hence , these options can be eliminated as well .
Answer C
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Re: $2,000 is deposited in a savings account that pays 6% annual interest  [#permalink]

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New post 26 Jan 2016, 03:52
this is the case of semi-annual compounding so, multiply time period by 2 and divide rate by 2
So,
new time=2periods and new rate=6/2=3%
Now,
CA=2000(1+3/100)^2=$2121.80

Hence answer is C
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Re: $2,000 is deposited in a savings account that pays 6% annual interest  [#permalink]

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New post 28 Aug 2016, 07:46
The question is asking how much worth is 2000 deposited in an account that pays 6% interest compounded semi annually.
Ok so we know that 6% of 2000 = 120 (since 1% is 20).
So if the compounding would have been done annually, then the amount in end is 2120. But because of compounding twice, the amount will be larger than this figure.
The next answer choice that is closest is choice C. D is too far. We can easily pick C
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Re: $2,000 is deposited in a savings account that pays 6% annual interest  [#permalink]

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New post 10 Sep 2018, 11:07
FV = P (1+r/n)^nt

FV = future value of the deposit 
P = principal or amount of money deposited 
r = annual interest rate (in decimal form)
n = number of times compounded per year
t = time in years.
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Re: $2,000 is deposited in a savings account that pays 6% annual interest &nbs [#permalink] 10 Sep 2018, 11:07
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