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

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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. 3
B. 4
C. 6
D. 9
E. 12

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

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Let the initial amount = p
After 'n' years, Amount = p(1 + 34.1/100)^n = p(1.341)^n

When n = 2, Amount = 1.75p approx
When n = 4, Amount = 3.06p approx
--> n = 4

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

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For simplicity of calculation, I would approximate 34.1% to 34%.

After year 1, The total amount will be 1.34 times the invested amount
After year 2, the total amount will be 1.34*1.34 = 1.7956 approximately 1.80 times the invested amount
After year 3, the total amount will be 1.34*1.80 = 2.412, approximately 2.4 times the invested amount
After year 4, the total amount will be 1.34*2.4 = 3.216, and this is more than 3 times the invested amount.

Therefore the amount has to be invested for at least 4 years at the compound annual interest rate of 34.1% in order to just earn more than three times the invested amount.

PS. I would be looking forward to shorter alternatives, as this approach is not optimal in my view.
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Re: An investment compounds annually at an interest rate of 34.1% What is  [#permalink]

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Initial Investment be x
Total amount = x(1.34)^y
Where y is time of investment
Above value have to become 3x
= (1.34*1.34*1.34*1.34) = 3.22x

So y have to be 4

OA:B

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

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CI=p*(1+r/100)'t
so R=34.1%
P=1 target P =4
will happen
IMO B

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. 3
B. 4
C. 6
D. 9
E. 12

Originally posted by Archit3110 on 15 Oct 2019, 00:57.
Last edited by Archit3110 on 15 Oct 2019, 21:23, edited 1 time in total.
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Re: An investment compounds annually at an interest rate of 34.1% What is  [#permalink]

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Quote:
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. 3
B. 4
C. 6
D. 9
E. 12

34.1% is close to 33.3% = 1/3

$$(1+1/3)^n≥3…(4/3)^n≥3$$
$$n=3…(4/3)^3=64/27<3$$
$$n=4…(4/3)^4=256/81=aprox.260/80=aprox.26/8>3$$

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

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Quote:
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. 3
B. 4
C. 6
D. 9
E. 12

Let the principal amount be p and time period of investment be t.
So, 3p=p$$(1+\frac{34.1}{100})^t$$
=> 3=$$(\frac{134.1}{100})^t$$
=>3=$$(1.341)^t$$
For t=3, $$(1.341)^t$$=2.41 and for t=4, $$(1.341)^t$$=3.23
Thus, smallest investment period is 4 years.

Therefore, the correct answer is option B.
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Re: An investment compounds annually at an interest rate of 34.1% What is  [#permalink]

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Imo. B

Initial investment = p, final amount (triple) = 3p, r = 34.1 % and n=?

3p = p (1+34.1/100)n
3 = (1.341)n, as p cancels out from the equation
Let's workout from answer choices to get the answer in quickest way,
Let's try, n=3, 1.3(41)*1.3 = 1.69, 1.69*1.3 = 1.6 * 1.3 = 2.xy, So, A is not the answer
Let's try, n=4, 1.34*1.34 = ~ 1.8, 1.8*1.8 = 3.xy, So, B can be answer.
Rest options are greater than 4, hence, it can satisfy the equation. But, we need smallest investment period to triple the investment. Hence, n = 4.

A. 3
B. 4
C. 6
D. 9
E. 12
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Re: An investment compounds annually at an interest rate of 34.1% What is  [#permalink]

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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. 3
B. 4
C. 6
D. 9
E. 12

Here Rule of 72 can be applied. The rule states that number '72' if divided by number of interest rate(34.1) would give a number of period in which the investment amount doubles. So to triple the investment amount we simply multiple the resultant number by 3/2. Hence

$$\frac{72}{34.1} * \frac{3}{2}$$ = 3.16

Since our investment period is annual, the smallest investment period is 4.

Alternatively,

Let investment = 100
Rate r = 34.1%
Initial amount = 100
Amount after 1st year = 134.1
Amount after 2nd year = 179.8
Amount after 3rd year = 241.1
Amount after 4th year = 323.3 (more than triple)

P.S.: In finance rule of 72 is not accurate so other measures are taken to make it as accurate as possible
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Re: An investment compounds annually at an interest rate of 34.1% What is  [#permalink]

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2 times: 134.1*1.341 approximately 180
3 times: 180*1.341 is approximately 240
Therefore 4 times to get more than 300%

B Re: An investment compounds annually at an interest rate of 34.1% What is   [#permalink] 15 Oct 2019, 19:17
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