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If money is invested at r percent interest, compounded annua

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If money is invested at r percent interest, compounded annua  [#permalink]

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New post 17 Dec 2012, 05:46
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If money is invested at r percent interest, compounded annually, the amount of the investment will double in approximately 70/r years. If Pat's parents invested $5,000 in a long-term bond that pays 8 percent interest, compounded annually, what will be the approximate total amount of the investment 18 years later, when Pat is ready for college?

(A) $20000
(B) $15000
(C) $12000
(D) $10000
(E) $9000
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Re: If money is invested at r percent interest, compounded annua  [#permalink]

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New post 17 Dec 2012, 05:48
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Walkabout wrote:
If money is invested at r percent interest, compounded annually, the amount of the investment will double in approximately 70/r years. If Pat's parents invested $5,000 in a long-term bond that pays 8 percent interest, compounded annually, what will be the approximate total amount of the investment 18 years later, when Pat is ready for college?

(A) $20000
(B) $15000
(C) $12000
(D) $10000
(E) $9000


Since investment doubles in 70/r years, then for r=8 it'll double in 70/8=~9 years (we are not asked about the exact amount so such an approximation will do). Thus in 18 years investment will double twice and become ($5,000*2)*2=$20,000 (after 9 years investment will become $5,000*2=$10,000 and in another 9 years it'll become $10,000*2=$20,000).

Answer: A.
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Re: If money is invested at r percent interest, compounded annua  [#permalink]

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New post 25 Jun 2014, 22:37
It's very important to pay attention to the wordings as first I thought that the compound interest formula needs to be applied.

Though I read the question again and got it correct :)

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Re: If money is invested at r percent interest, compounded annua  [#permalink]

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New post 24 Aug 2014, 14:25
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I think without the 1st sentence, we still can guess the answer easily.

$5,000 at 8%/year = $400/year --> 10-years interest will be $4,000, 20 years will be $8,000
Since the interest compounded annually in 18 years (very long period), the total value would be >$18,000 --> eliminate B,C,D,E
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If money is invested at r percent interest, compounded annua  [#permalink]

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New post 10 Oct 2014, 19:42
If money is invested at r percent interest, compounded annually, the amount of the investment will double in approximately 70/r years. If Pat's parents invested $5,000 in a long-term bond that pays 8 percent interest, compounded annually, what will be the approximate total amount of the investment 18 years later, when Pat is ready for college?

(A) $20000
(B) $15000
(C) $12000
(D) $10000
(E) $9000


There has to be a logic to why they gave you "If money is invested at r percent interest, compounded annually, the amount of the investment will double in approximately 70/r years."

If r = 8%, the principal will double in 70/8 = apprx 9 years. So in 9 years, 5000 will become 10,000. In another 9 years (i.e. 18 years from now) principal will double again and become $20,000.
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Re: If money is invested at r percent interest, compounded annua  [#permalink]

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New post 21 Oct 2014, 23:35
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5000 will multiply approx. 4 times = 5000 * 4 = 20000

Answer = A
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If money is invested at r percent interest, compounded annually,  [#permalink]

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New post 03 Mar 2015, 22:12
Hey all,

Just wondering what in the question made you realise you should solve this question via 5,000 x 2 x 2 rather than using the actual interest formula? i.e. P(1+r/n)^nt?

I used the formula then realised the calcs were too complicated.

Thanks in advance for your help.
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Re: If money is invested at r percent interest compounded annual  [#permalink]

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New post 03 Mar 2015, 22:35
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Hi ColdSushi,

GMAT Quant questions (and the accompanying answer choices) are always carefully written. Sometimes they offer hints as to how you can use estimation to get to the correct answer.

Here, the word 'approximate' in the prompt is essentially telling you to estimate an answer. With an interest rate of 8% and the given formula, you're meant to estimate that the investment will double in 70/8 = about 9 years. The question then asks for the total investment after 18 years. THAT number (18) is not an accident - it was specifically chosen so that you can take advantage of your estimation.

Start = $5000
After 9 years = $10,000
After 18 years = $20,000

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Re: If money is invested at r percent interest compounded annual  [#permalink]

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New post 04 Mar 2015, 16:30
EMPOWERgmatRichC wrote:
Hi ColdSushi,

GMAT Quant questions (and the accompanying answer choices) are always carefully written. Sometimes they offer hints as to how you can use estimation to get to the correct answer.

Here, the word 'approximate' in the prompt is essentially telling you to estimate an answer. With an interest rate of 8% and the given formula, you're meant to estimate that the investment will double in 70/8 = about 9 years. The question then asks for the total investment after 18 years. THAT number (18) is not an accident - it was specifically chosen so that you can take advantage of your estimation.

Start = $5000
After 9 years = $10,000
After 18 years = $20,000

Rich


Ah - ok thank you Rich. I def need to pay more attention to these hints.

I find myself 60-70% "there" in solving a question i.e. I'd know what the question is asking and the end point (as opposed to 15-20% "there" when I first started studying for the GMAT) but get stuck because I'd miss an important word or picked a harder way to approach a problem. Hopefully things will get better with practice!
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Re: If money is invested at r percent interest compounded annual  [#permalink]

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New post 23 Nov 2015, 13:00
ColdSushi wrote:
Hey all,

Just wondering what in the question made you realise you should solve this question via 5,000 x 2 x 2 rather than using the actual interest formula? i.e. P(1+r/n)^nt?

I used the formula then realised the calcs were too complicated.

Thanks in advance for your help.


Maybe because they said approximate and that they gave 70/r to help. Otherwise, goodluck computing a power of 18 without a calculator :P
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Re: If money is invested at r percent interest, compounded annua  [#permalink]

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New post 25 Dec 2015, 11:07
Hi All,

This question has some similarities to "symbolism" questions (in which the prompt shows you a "made up" symbol, tells you what it means and asks you to do a simple calculation with it). The easiest way to tackle the question is to simply follow the instructions.

We're told that r = percent interest.

We're also told that an investment with DOUBLE in approximately 70/r years.

We're told to invest $5,000 at 8 percent for 18 years.

Plug in r = 8

70/8 is about 9 years, meaning our investment will DOUBLE in 9 years.

In the first 9 years, $5,000 doubles to $10,0000
In the next 9 years, $10,000 doubles to $20,000

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Re: If money is invested at r percent interest, compounded annua  [#permalink]

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New post 16 Jun 2016, 05:11
Walkabout wrote:
If money is invested at r percent interest, compounded annually, the amount of the investment will double in approximately 70/r years. If Pat's parents invested $5,000 in a long-term bond that pays 8 percent interest, compounded annually, what will be the approximate total amount of the investment 18 years later, when Pat is ready for college?

(A) $20000
(B) $15000
(C) $12000
(D) $10000
(E) $9000


Although this question appears as if we may have to do a lot of calculating, we actually do not. Focus on the first sentence of the question stem. We are given that if money is invested at r percent interest, compounded annually, the amount of investment will double in approximately 70/r years. We are then given that Pat’s parents invest $5,000 at 8 percent interest. It follows that the investment will double after 70/8 years, which is roughly 9 years. With an initial investment of $5,000, the investment will double to $10,000 in about 9 years. In another 9 years (a total of 18 years) the investment will double again to about $20,000.

Answer A
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Re: If money is invested at r percent interest, compounded annua  [#permalink]

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New post 06 Apr 2018, 02:59
Bunuel wrote:
Walkabout wrote:
If money is invested at r percent interest, compounded annually, the amount of the investment will double in approximately 70/r years. If Pat's parents invested $5,000 in a long-term bond that pays 8 percent interest, compounded annually, what will be the approximate total amount of the investment 18 years later, when Pat is ready for college?

(A) $20000
(B) $15000
(C) $12000
(D) $10000
(E) $9000


Since investment doubles in 70/r years, then for r=8 it'll double in 70/8=~9 years (we are not asked about the exact amount so such an approximation will do). Thus in 18 years investment will double twice and become ($5,000*2)*2=$20,000 (after 9 years investment will become $5,000*2=$10,000 and in another 9 years it'll become $10,000*2=$20,000).

Answer: A.


Bunuel isnt the question asking to calculate the total sum (invested ammound +interest rate) like this \(x = 5000(1+0.08)^9\) :? where doest say that we need to calculate only amount ivested :? i am kinda condused
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Re: If money is invested at r percent interest, compounded annua  [#permalink]

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New post 06 Apr 2018, 03:10
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dave13 wrote:
Bunuel wrote:
Walkabout wrote:
If money is invested at r percent interest, compounded annually, the amount of the investment will double in approximately 70/r years. If Pat's parents invested $5,000 in a long-term bond that pays 8 percent interest, compounded annually, what will be the approximate total amount of the investment 18 years later, when Pat is ready for college?

(A) $20000
(B) $15000
(C) $12000
(D) $10000
(E) $9000


Since investment doubles in 70/r years, then for r=8 it'll double in 70/8=~9 years (we are not asked about the exact amount so such an approximation will do). Thus in 18 years investment will double twice and become ($5,000*2)*2=$20,000 (after 9 years investment will become $5,000*2=$10,000 and in another 9 years it'll become $10,000*2=$20,000).

Answer: A.


Bunuel isnt the question asking to calculate the total sum (invested ammound +interest rate) like this \(x = 5000(1+0.08)^9\) :? where doest say that we need to calculate only amount ivested :? i am kinda condused


The question asks to find the approximate total amount of the investment in 18 years. So, (initial investment) + (interest earned in 18 years). If you use interests formula it's \(5000(1+0.08)^{18} \approx 19,980\). The question also gives a way to calculate this quicker by saying that "if money is invested at r percent interest, compounded annually, the amount of the investment will double in approximately 70/r years", which all the solutions above used to get the answer.
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