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# a savings account

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Senior Manager
Joined: 07 Nov 2009
Posts: 313
Followers: 6

Kudos [?]: 243 [0], given: 20

a savings account [#permalink]  21 Jul 2010, 21:34
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Difficulty:

(N/A)

Question Stats:

0% (00:00) correct 100% (02:52) wrong based on 3 sessions
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?$1500
$1750$2000
$2500$3000

The formula for calculating compound interest is A = P(1 + r/n)nt where the variables represent the following:
A = amount of money accumulated after t years (principal + interest)
P = principal investment
r = interest rate (annual)
n = number of times per year interest is compounded
t = number of years
[Reveal] Spoiler: OA
Manager
Joined: 20 Jul 2010
Posts: 198
Followers: 2

Kudos [?]: 69 [0], given: 7

Re: a savings account [#permalink]  21 Jul 2010, 23:06
IMO D
rohitgoel15 wrote:
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?$1500
$1750$2000
$2500$3000

The formula for calculating compound interest is A = P(1 + r/n)nt where the variables represent the following:
A = amount of money accumulated after t years (principal + interest)
P = principal investment
r = interest rate (annual)
n = number of times per year interest is compounded
t = number of years

Solution:
r = Rate = 8% compounded quarterly.. = 2% per quarter
t = 6 motnhs = 2 quarters
So A = P (1+0.02)^2
=> A = P * 1.0404

Subsitute, P for 1500, 1700, 2000.. The A-P should be greater than 100 (since Interest = Amount - principal).
For 2500, interest is 101...

Hence, D
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Concentration: Technology, Entrepreneurship
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Kudos [?]: 1214 [0], given: 235

Re: a savings account [#permalink]  21 Jul 2010, 23:20
A = P(1 + r/n)nt here t =1/2 and n=4
=> A = P(1 + 8 %/4)4*(1/2)
=> A = P(1 + 2%)^2
=> A = P ( 1+ (2%)^2 + 4%) ,(2%)^2 is very small and can be ignored

=> A = P ( 1+4%) => A-P = P*4%
Also A-P = 100 => P = 100/4% = 100*100/4 = 2500
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Re: a savings account   [#permalink] 21 Jul 2010, 23:20
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