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An investment compounds annually at an interest rate of 34.1% What is

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An investment compounds annually at an interest rate of 34.1% What is  [#permalink]

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New post 14 Feb 2011, 19:25
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An investment compounds annually at an interest rate of 34.1% What is the smallest investment period by which time the investment will more than triple in value?

A. 4
B. 5
C. 6
D. 7
E. 8

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Re: An investment compounds annually at an interest rate of 34.1% What is  [#permalink]

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New post 15 Feb 2011, 06:39
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By the Compound Interest formula :

\(A = P(1 + r/100)^nt\)

It comes to (1.341)^n = 3 (since A = 3P, and t = 1)

On multiplying 1.341 further with itself, it can be seen that n = 4, so answer is A.
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Re: An investment compounds annually at an interest rate of 34.1% What is  [#permalink]

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New post 15 Feb 2011, 07:24
Please correct me if I am wrong but it seems you need to workout the multiplication of 1.341 at least 3 times very quickly which seems rather daunting given the tight time constraints of the GMAT..

Is there a faster way of doing this?
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Re: An investment compounds annually at an interest rate of 34.1% What is  [#permalink]

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New post 15 Feb 2011, 09:29
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drifting wrote:
Please correct me if I am wrong but it seems you need to workout the multiplication of 1.341 at least 3 times very quickly which seems rather daunting given the tight time constraints of the GMAT..

Is there a faster way of doing this?


I agree; I divided the principal by 3 by considering approx 33.33% and rounded the value to greater nearest integer;

1 year: 100/3 = 33.33 approx $34: Total: 134
2nd year: 134/3 = 45: Total: 134+45 = 179
3rd year: 179/3 = 60: Total: 179+60 = 239
4th year: 239/3 = 80: Total: 239+80 = 319 > 3(100)

;4 years;

Perhaps there is a better way...
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Re: An investment compounds annually at an interest rate of 34.1% What is  [#permalink]

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New post 15 Feb 2011, 19:22
Please explain this bit :

"I divided the principal", i.e, how does division of principal yield interest ?
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New post 15 Feb 2011, 19:58
I rounded to 33.3333% or 1/3

Since the formula is:

P1 = P0 (1 + r)^n

3 = 1(1+.333333333)^n

3 = 1(4/3)^n

3= (4^n / 3^n)

From here, start with n = 4 and see if the ratio is greater or less than 3

4^4 = 16^2 = 256
3^4 = 9^2 = 81

81*3 = 243...256>243 so 4 is sufficient if the rate were 33.333%. Since the rate is larger than 33.33% it is definitely sufficient
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Re: An investment compounds annually at an interest rate of 34.1% What is  [#permalink]

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New post 15 Feb 2011, 23:07
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subhashghosh wrote:
Please explain this bit :

"I divided the principal", i.e, how does division of principal yield interest ?


We can quickly get the percentage if we divide the number for which the percentage is found:
such as,
20% of 40 = 40/5 = 8
10% of 80 = 80/10 = 8
50% of 35 = 35/2 = 17.5
33.33% of 100 = 100/3 = 33 approx

Since 34.1% is close to 33.33%; we can divide the number(or principal by 3 and get the interest); Investment: $100

1st year: 34.1% interest is gotten back on 100: 100/3 = 33.33 approx $34: New principal becomes: Principal+Interest: 100+34=134

2nd year: 34.1% interest on 134; 134/3 = 45: Total: 134+45 = 179(new principal)
3rd year: 179/3 = 60: Total: 179+60 = 239
4th year: 239/3 = 80: Total: 239+80 = 319 > 3(100); end of 4 years, the return was already more than triple.
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Re: An investment compounds annually at an interest rate of 34.1% What is  [#permalink]

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New post 17 Feb 2011, 04:38
subhashghosh wrote:
By the Compound Interest formula :

\(A = P(1 + r/100)^nt\)

It comes to (1.341)^n = 3 (since A = 3P, and t = 1)

On multiplying 1.341 further with itself, it can be seen that n = 4, so answer is A.


Thanks for the explanation!

But what if this equation consists of a number larger than 3, say 300!

Another question, Is the T in your formula really necessary?
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Re: An investment compounds annually at an interest rate of 34.1% What is  [#permalink]

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New post 17 Feb 2011, 08:55
I liked this approach. This question is not difficult, but with this approach it can be done more quickly as well.

fluke wrote:
drifting wrote:
Please correct me if I am wrong but it seems you need to workout the multiplication of 1.341 at least 3 times very quickly which seems rather daunting given the tight time constraints of the GMAT..

Is there a faster way of doing this?


I agree; I divided the principal by 3 by considering approx 33.33% and rounded the value to greater nearest integer;

1 year: 100/3 = 33.33 approx $34: Total: 134
2nd year: 134/3 = 45: Total: 134+45 = 179
3rd year: 179/3 = 60: Total: 179+60 = 239
4th year: 239/3 = 80: Total: 239+80 = 319 > 3(100)

;4 years;

Perhaps there is a better way...
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Re: An investment compounds annually at an interest rate of 34.1% What is  [#permalink]

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New post 01 Dec 2016, 18:25
100(1+0.341)^t = 301
(1.341)^t=3.01
t ln(1.341) = ln(3.01)
t = ~3.76

4 is closest to this choice.

A.
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Re: An investment compounds annually at an interest rate of 34.1% What is  [#permalink]

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New post 04 Dec 2016, 05:39
1
I used the approximation to 1/3 and I started with a capital of 10

1)10--13
2)13--17
3)17--23
4)23--30+

So answer is A. I reckon in these cases approximation and easy numbers are the only way
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Re: An investment compounds annually at an interest rate of 34.1% What is  [#permalink]

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New post 13 Jan 2018, 09:48
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bhandariavi wrote:
An investment compounds annually at an interest rate of 34.1% What is the smallest investment period by which time the investment will more than triple in value?

A. 4
B. 5
C. 6
D. 7
E. 8


We can use fractions to solve this question.

Each year, the investment increases 34.1%
This is very close to an increase of 1/3 (33.33%)

So, if the investment increases by 1/3 each year, then each year, we can find the value of the investment by multiplying last year's value by 4/3 (this represents a 1/3 increase)

So, let's say the initial investment is $1.
We want to determine how many years it takes the investment to be worth at least $3 (triple)

Year 0: $1
Year 1: ($1)(4/3) = $4/3
Year 2: ($1)(4/3)(4/3) = $16/9 (this is less than $3)
Year 3: ($1)(4/3)(4/3)(4/3) = $64/27 (this is less than $3)
Year 4: ($1)(4/3)(4/3)(4/3)(4/3) = $256/81 (this is more than $3)

So, it takes 4 years for the investment to more than triple in value.

Answer = A

Cheers,
Brent
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An investment compounds annually at an interest rate of 34.1% What is  [#permalink]

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New post 18 May 2018, 10:27
bhandariavi wrote:
An investment compounds annually at an interest rate of 34.1% What is the smallest investment period by which time the investment will more than triple in value?

A. 4
B. 5
C. 6
D. 7
E. 8


The annually compounded interest formula is A = P(1 + r)^t. Since we want to triple the value of investment, A = 3P. So we have:

3P = P(1 + 0.341)^t

Divide both sides by P, we have:

3 = (1.341)^t

Let’s round the base to 1.333 = 4/3. We see that (4/3)^3 = 64/27 < 3 but (4/3)^4 = 256/81 > 3. So t must be 4.

Answer: A
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