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a savings account

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a savings account [#permalink]

21 Jul 2010, 22:34

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0% (00:00) correct

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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?
$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

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Re: a savings account [#permalink]

22 Jul 2010, 00:06

IMO D

rohitgoel15 wrote:

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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Re: a savings account [#permalink]

22 Jul 2010, 00:20

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] 22 Jul 2010, 00:20

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