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On a certain date, Pat invested $10,000 at x percent annual [#permalink]

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22 Jul 2008, 18:59

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On a certain date, Pat invested $10,000 at x percent annual interest, compounded annually. If the total value of the investment plus interest at the end of 12 years will be $40,000, in how many years, the total value of the investment plus interest will increase to $80,000?

Re: On a certain date, Pat invested $10,000 at x percent annual [#permalink]

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22 Jul 2008, 21:13

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arjtryarjtry wrote:

On a certain date, Pat invested $10,000 at x percent annual interest, compounded annually. If the total value of the investment plus interest at the end of 12 years will be $40,000, in how many years, the total value of the investment plus interest will increase to $80,000? A. 15 B. 16 C. 18 D. 20 E. 24

40.000=10.000 . (1+x)^12 => 4= (1+x)^12 =>2= (1+x)^6 => 8 = (1+x)^ 18 So, after 18 years, the total value of the investment plus interest will increase to $80,000.

Re: On a certain date, Pat invested $10,000 at x percent annual [#permalink]

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02 Sep 2008, 19:50

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This post was BOOKMARKED

On a certain date, Pat invested $10,000 at x percent annual interest, compounded annually. If the total value of the investment plus interest at the end of 12 years will be $40,000, in how many years, the total value of the investment plus interest will increase to $80,000? A. 15 B. 16 C. 18 D. 20 E. 24

for compound interest problems, when the time is large, then how does one approach???

dont just give the steps... also mention, for variations in the problems, how does one approach???

Re: On a certain date, Pat invested $10,000 at x percent annual [#permalink]

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02 Sep 2008, 23:24

arjtryarjtry wrote:

On a certain date, Pat invested $10,000 at x percent annual interest, compounded annually. If the total value of the investment plus interest at the end of 12 years will be $40,000, in how many years, the total value of the investment plus interest will increase to $80,000? A. 15 B. 16 C. 18 D. 20 E. 24

for compound interest problems, when the time is large, then how does one approach???

dont just give the steps... also mention, for variations in the problems, how does one approach???

your second post blocked my post.

i cannot do it without calculator or computer and also beleieve this is not real gmat type question cuz its very difficult to get the value without those machines.

if i were to choose during the test, would go for 18/ or 20. probably 18 cuz not it wont take too long to get the value doubled....
_________________

Re: On a certain date, Pat invested $10,000 at x percent annual [#permalink]

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03 Sep 2008, 06:31

1

This post received KUDOS

arjtryarjtry wrote:

On a certain date, Pat invested $10,000 at x percent annual interest, compounded annually. If the total value of the investment plus interest at the end of 12 years will be $40,000, in how many years, the total value of the investment plus interest will increase to $80,000? A. 15 B. 16 C. 18 D. 20 E. 24

for compound interest problems, when the time is large, then how does one approach???

dont just give the steps... also mention, for variations in the problems, how does one approach???

Re: On a certain date, Pat invested $10,000 at x percent annual [#permalink]

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03 Sep 2008, 12:47

2

This post was BOOKMARKED

arjtryarjtry wrote:

On a certain date, Pat invested $10,000 at x percent annual interest, compounded annually. If the total value of the investment plus interest at the end of 12 years will be $40,000, in how many years, the total value of the investment plus interest will increase to $80,000? A. 15 B. 16 C. 18 D. 20 E. 24

for compound interest problems, when the time is large, then how does one approach???

dont just give the steps... also mention, for variations in the problems, how does one approach???

Let's simplify this question.

First equation; 40,000 = 10,000(1 + x)^12 Given that (1 + x) = a and rearrange the equation above we get 4 = a^12 = 2^2 So now we know that a^12 = (a^6)^2 = 2^2 Therefore, (a^6) = 2

Re: On a certain date, Pat invested $10,000 at x percent annual [#permalink]

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03 Sep 2008, 13:42

Even though it looks like a tough question, it is actually not. 4 times in 12 yesrs = > 2 times in 6 years ( from 40K to 80K ). So total year = 12 +6 =18

Re: On a certain date, Pat invested $10,000 at x percent annual [#permalink]

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02 Feb 2009, 08:51

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GMAT TIGER wrote:

arjtryarjtry wrote:

On a certain date, Pat invested $10,000 at x percent annual interest, compounded annually. If the total value of the investment plus interest at the end of 12 years will be $40,000, in how many years, the total value of the investment plus interest will increase to $80,000? A. 15 B. 16 C. 18 D. 20 E. 24

for compound interest problems, when the time is large, then how does one approach???

dont just give the steps... also mention, for variations in the problems, how does one approach???

your second post blocked my post.

i cannot do it without calculator or computer and also beleieve this is not real gmat type question cuz its very difficult to get the value without those machines.

if i were to choose during the test, would go for 18 or 20. probably 18 cuz it wont take too long to get the value doubled....

I found a method: Rule of 72.

Given an x% return, it takes 10,000 to quadralope 12 years.

So according to the rule: 72/x is the no of years 10,000.00 took to double 20,000.00. Again, 20,000.00 took to double 40,000.00 same (72/x) no of years.

72/x+ 72/x = 12 x = 12% (though rate here is not very much required).

Again, 40,000.00 takes the same (72/x) no of years to double 80,000.00.

72/x = 6 years.

So altogather: 10,000 - 20,000 = 6 years 20,000 - 40,000 = 6 years 40,000 - 80,000 = 6 years total 18 years.
_________________

Re: On a certain date, Pat invested $10,000 at x percent annual [#permalink]

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02 Jul 2014, 06:45

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Re: On a certain date, Pat invested $10,000 at x percent annual [#permalink]

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12 Dec 2015, 11:33

i tried different approaches, but I believe this is the most straight forward one. in 12y, the amount is 4x, where x is the initial amount. it means that if we start with 40k in year 12, in another 12 years, we'll have 160k. we can eliminate right away 24 years. now, if the amount 4x in 12y, it might be true that the amount will be 2x in 6y. ok, so we have 12y initial, then another 6 years, so total 18 years to reach 80k. C.