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GRE Prep Club Team Member
Joined: 20 Feb 2017
Posts: 2508
Given Kudos: 1053
GPA: 3.39
Donald plans to invest x dollars in a savings account that pays intere
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11 Mar 2022, 10:08
11 Mar 2022, 10:08
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Expert Reply
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Question Stats:
61% (02:12) correct
38% (02:17) wrong based on 21 sessions
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Donald plans to invest x dollars in a savings account that pays interest at an annual rate of 8% compounded quarterly. Approximately what amount is the minimum that Donald will need to invest to earn over $100 in interest within 6 months?
A. 1500
B. 1750
C. 2000
D. 2500
E. 3000
A. 1500
B. 1750
C. 2000
D. 2500
E. 3000
GRE Prep Club Team Member
Joined: 20 Feb 2017
Posts: 2508
Given Kudos: 1053
GPA: 3.39
Re: Donald plans to invest x dollars in a savings account that pays intere
[#permalink]
12 Mar 2022, 22:04
12 Mar 2022, 22:04
1
Expert Reply
Answer = D = 2500
For small amount, small duration (in 6 months), with quarterly compounding, there would be hardly major difference between SI & CI.
We can safely use the SI formula after proper adjustments
SI = 100
Principal = p (Required to be calculated)
RoI = 8% PA = 4% for 6 months
\(100 = p * \frac{4}{100}\)
\(p = \frac{100*100}{4} = 2500\)
For small amount, small duration (in 6 months), with quarterly compounding, there would be hardly major difference between SI & CI.
We can safely use the SI formula after proper adjustments
SI = 100
Principal = p (Required to be calculated)
RoI = 8% PA = 4% for 6 months
\(100 = p * \frac{4}{100}\)
\(p = \frac{100*100}{4} = 2500\)
Re: Donald plans to invest x dollars in a savings account that pays intere
[#permalink]
16 May 2024, 02:28
16 May 2024, 02:28
1
Compound interest formula:
x*(1 + (0.08/4)^2 ---- because the interest compounds quarterly, we divide the percent by 8, and since the time is 6 months, it will compound two times (1 quarter = 3 months)
x*(1 + (0.08/4)^2 = x+100 (we need to earn $100 profit)
(1 + (0.08/4)^2 = (x+100)/x
(1 + (0.02)^2 = 1 + 100/x
1.0404 = 1 + 100/x
0.0404 = 100/x
x = approximately 2 475
The closest answer is D.
x*(1 + (0.08/4)^2 ---- because the interest compounds quarterly, we divide the percent by 8, and since the time is 6 months, it will compound two times (1 quarter = 3 months)
x*(1 + (0.08/4)^2 = x+100 (we need to earn $100 profit)
(1 + (0.08/4)^2 = (x+100)/x
(1 + (0.02)^2 = 1 + 100/x
1.0404 = 1 + 100/x
0.0404 = 100/x
x = approximately 2 475
The closest answer is D.
