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# Amy deposited $1,000 into an account that earns 8% annual in  Question banks Downloads My Bookmarks Reviews Important topics Author Message TAGS: Retired Moderator Joined: 07 Jun 2014 Posts: 4803 GRE 1: Q167 V156 WE: Business Development (Energy and Utilities) Followers: 175 Kudos [?]: 3037 [0], given: 394 Amy deposited$1,000 into an account that earns 8% annual in [#permalink]  27 Jul 2018, 07:04
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Question Stats:

62% (01:40) correct 37% (02:51) wrong based on 27 sessions
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 [Reveal] Spoiler: OA _________________ Sandy If you found this post useful, please let me know by pressing the Kudos Button Try our free Online GRE Test Retired Moderator Joined: 07 Jun 2014 Posts: 4803 GRE 1: Q167 V156 WE: Business Development (Energy and Utilities) Followers: 175 Kudos [?]: 3037 [1] , given: 394 Re: Amy deposited$1,000 into an account that earns 8% annual in [#permalink]  12 Aug 2018, 05:02
1
KUDOS
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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 $$\1,020 \times 1.02 = \1,040.40$$. _________________ Sandy If you found this post useful, please let me know by pressing the Kudos Button Try our free Online GRE Test Re: Amy deposited$1,000 into an account that earns 8% annual in   [#permalink] 12 Aug 2018, 05:02
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