GRE Prep Club Daily Prep
Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.
Customized
for You
Track
Your Progress
Practice
Pays
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
Amy deposited $1,000 into an account that earns 8% annual in
[#permalink]
27 Jul 2018, 07:04
27 Jul 2018, 07:04
1
Expert Reply
6
Bookmarks
00:00
Question Stats:
68% (01:59) correct
31% (02:36) wrong based on 67 sessions
Hide Show timer Statistics
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
[#permalink]
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
[#permalink]
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).
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.
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.
