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Amy deposited $1,000 into an account that earns 8% annual in
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27 Jul 2018, 07:04
27 Jul 2018, 07:04
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Question Stats:
69% (01:58) correct
30% (02:36) wrong based on 68 sessions
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Amy deposited $1,000 into an account that earns 8% annual interest compounded every 6 months.Bob deposited $1,000 into an account that earns 8% annual interest compounded quarterly. If neither Amy nor Bob make any additional deposits or withdrawals, in 6 months how much more money will Bob have in his account than will Amy have in hers?
(A) $40
(B) $8
(C) $4
(D) $0.40
(E) $0.04
(A) $40
(B) $8
(C) $4
(D) $0.40
(E) $0.04
Re: Amy deposited $1,000 into an account that earns 8% annual in
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12 Aug 2018, 05:02
12 Aug 2018, 05:02
3
Expert Reply
Explanation
Both Amy and Bob start with $1,000 and earn 8% interest annually; the difference is in how often this interest is compounded. Amy’s interest is compounded twice a year at 4% each time (8% annual interest compounded 2 times a year means that she gets half the interest, or 4%, every 6 months).
Bob’s interest is compounded four times a year at 2% (8% divided by 4 times per year) each time. After 6 months, Amy has \(\$1,000 \times 1.04 = \$1,040.00\) (one interest payment at 4%) and Bob has \(\$1,000 \times (1.02)^2 = $1,040.40\) (two interest payments at 2%). The difference is \(\$1,040.40 – \$1,040.00 = \$0.40\).
Alternatively, Bob’s interest could be calculated as two separate payments. After three months, Bob will have \(\$1,000 \times 1.02 = \$1,020.00\). After 6 months, Bob will have \(\$1,020 \times 1.02 = \$1,040.40\).
Both Amy and Bob start with $1,000 and earn 8% interest annually; the difference is in how often this interest is compounded. Amy’s interest is compounded twice a year at 4% each time (8% annual interest compounded 2 times a year means that she gets half the interest, or 4%, every 6 months).
Bob’s interest is compounded four times a year at 2% (8% divided by 4 times per year) each time. After 6 months, Amy has \(\$1,000 \times 1.04 = \$1,040.00\) (one interest payment at 4%) and Bob has \(\$1,000 \times (1.02)^2 = $1,040.40\) (two interest payments at 2%). The difference is \(\$1,040.40 – \$1,040.00 = \$0.40\).
Alternatively, Bob’s interest could be calculated as two separate payments. After three months, Bob will have \(\$1,000 \times 1.02 = \$1,020.00\). After 6 months, Bob will have \(\$1,020 \times 1.02 = \$1,040.40\).
Re: Amy deposited $1,000 into an account that earns 8% annual in
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10 Dec 2023, 10:57
10 Dec 2023, 10:57
Hello from the GRE Prep Club BumpBot!
Thanks to another GRE Prep Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).
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Thanks to another GRE Prep Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).
Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
