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26 Jan 2016, 02:49
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C
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Difficulty:
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71% (01:18) correct
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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
A. $2,060
B. $2,120
C. $2,122
D. $2,247
E. $2,258
26 Jan 2016, 04:23
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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
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
26 Jan 2016, 04:52
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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
So,
new time=2periods and new rate=6/2=3%
Now,
CA=2000(1+3/100)^2=$2121.80
Hence answer is C
