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# Jeff opens a savings account with a 3000,- USD deposit and

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Intern
Joined: 14 Jul 2006
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Jeff opens a savings account with a 3000,- USD deposit and [#permalink]  28 Jul 2006, 03:04
"Jeff opens a savings account with a 3000,- USD deposit and makes no other deposit or withdrawals. The account pays interest at the rate of 6% compounded monthly. How much money rounded up to the nearest dollar, is in the account at the end of year 1?"

Any body a quick way to solve that?
Director
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The quickest way for me would be to take 6% interest of 3000, which would equal 3000*0.06=180, so the whole sum would be 3180 and i would choose a bit bigger value than this from the answer choices....
Intern
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True but if I need to calculate the exact amount because 2 choices would be left, what would be the quickest way to do so?

SimaQ wrote:
The quickest way for me would be to take 6% interest of 3000, which would equal 3000*0.06=180, so the whole sum would be 3180 and i would choose a bit bigger value than this from the answer choices....
CEO
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Sum at the end of year = 3000 *(1+0.06)^12

Problem is to get (1+0.06)^12
Let x = 1 and y = 0.06
(x+y)^12 = [(x+y)^3]^4

(x+y)^3 = x^3+y^3+3yx^2 + 3xy^2
discard terms with y^3 and y^2 because they will be very small.
we get 1 + 3*0.06 = 1.18 approx = 1.2
now calculate (1.2)^4 = 1.44^2 to compensate for gain in 1.18 make 1.44 as 1.4.
Now we get 1.4^2 = 1.96 i.e approx 2.
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Manager
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ps, good approach for estimating this beast. Except that the correct formula is not (1+0.06)^12 but (1+0.06/12)^12.

On the test day, if there is no clear winner among choices, I would probably narrow it down to 2 choices and take a guess. Too much time can be spend on these calculations. Not worth it, IMHO
CEO
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v1rok wrote:
Except that the correct formula is not (1+0.06)^12 but (1+0.06/12)^12.

Thanks buddy. I thought intrest rate is 6% monthly.
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Senior Manager
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You get 1/2 of a percent monthly compounded. How to do it quickly, I do not know. So you would get 15 dollars a month in simple interest. Then you have to compound the extra each month...yeah I guess it is pretty difficult

If you compound it only six times it gets easier as it is one percent...then just make it a bit higher than that.
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Re: Compounded interest - Jeff kills me [#permalink]  28 Jul 2006, 22:15
Tutuca wrote:
"Jeff opens a savings account with a 3000,- USD deposit and makes no other deposit or withdrawals. The account pays interest at the rate of 6% compounded monthly. How much money rounded up to the nearest dollar, is in the account at the end of year 1?"

Any body a quick way to solve that?

if 6% is your monthly rate, this is the quickest approach: = 3,000 x 2 = 6,000.

its a tricky question.

we can also use here "rule of 72". if rate is 6% monthly, then it takes 72/6 = 12 months to doubled 3,000. so after 12 months, it will be 6,000.
Director
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Re: Compounded interest - Jeff kills me [#permalink]  31 Jul 2006, 03:36
MA wrote:
Tutuca wrote:
"Jeff opens a savings account with a 3000,- USD deposit and makes no other deposit or withdrawals. The account pays interest at the rate of 6% compounded monthly. How much money rounded up to the nearest dollar, is in the account at the end of year 1?"

Any body a quick way to solve that?

if 6% is your monthly rate, this is the quickest approach: = 3,000 x 2 = 6,000.

its a tricky question.

we can also use here "rule of 72". if rate is 6% monthly, then it takes 72/6 = 12 months to doubled 3,000. so after 12 months, it will be 6,000.

I think 6% is yearly not monthly here.....

The answer would be more than 3180 as i explained it earlier.....
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A = 3000(1+(6/12)/100) ^ 12
= 3000 (1 + 1/200) ^12
= 3000(201/200) ^12

I would chose something closer to 3000 as 201 /200 ~ 1
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