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Money invested at x%, compounded annually, triples in value in approxi

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Money invested at x%, compounded annually, triples in value in approxi  [#permalink]

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Money invested at x%, compounded annually, triples in value in approximately every 112/x years. If $2500 is invested at a rate of 8%, compounded annually, what will be its approximate worth in 28 years?

A. $3,750
B. $5,600
C. $8,100
D. $15,000
E. $22,500


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Re: Money invested at x%, compounded annually, triples in value in approxi  [#permalink]

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New post 25 Aug 2015, 00:57
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Bunuel wrote:
Money invested at x%, compounded annually, triples in value in approximately every 112/x years. If $2500 is invested at a rate of 8%, compounded annually, what will be its approximate worth in 28 years?

A. $3,750
B. $5,600
C. $8,100
D. $15,000
E. $22,500


Ans: E

Solution: money compounded annually at x% triples in 112/x years.

we need to find the final amount of 2500 at the end of the 28 years.. compounded annually at 8%
by putting the value in formula it will give us = 2500(1.08)^28

there must be a relation between these two conditions?
x= 8% so money will triple in 112/8 = 14 years
so money will be 3^2 = 9 times in 28 years
so 2500*9 = 22500 Ans
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Re: Money invested at x%, compounded annually, triples in value in approxi  [#permalink]

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New post 25 Aug 2015, 04:27
\(\frac{28}{y}\), where \(y\) is number of years in order to triple value
\(\frac{112}{x}\), where \(x\) is the discount rate
Thus, \(x=14\) and \(y=2\) and therefore \((2500*3)*3=(7500*3)=22500\)
IMO E.

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Re: Money invested at x%, compounded annually, triples in value in approxi  [#permalink]

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New post 25 Aug 2015, 08:20
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112/8 = 14 years to triple
so 2500 x 3 = 7500

but question asks for 28 years which is another run of 14 years from original 2500
so 7500 x 3 = 22500
ans E
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Re: Money invested at x%, compounded annually, triples in value in approxi  [#permalink]

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New post 25 Aug 2015, 10:56
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Principal triples every 112/x years
P(Triples)^(Years/Rate)
2500(3)^(28*8/112)=2500(3)^(2)=22500
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Re: Money invested at x%, compounded annually, triples in value in approxi  [#permalink]

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New post 25 Aug 2015, 11:27
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= 2500 x (1+8%)^(224/8) = 7500 * (1+8%)^(112/8) = 7500 x 3 = 22500.
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Re: Money invested at x%, compounded annually, triples in value in approxi  [#permalink]

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New post 25 Aug 2015, 11:32
Bunuel wrote:
Money invested at x%, compounded annually, triples in value in approximately every 112/x years. If $2500 is invested at a rate of 8%, compounded annually, what will be its approximate worth in 28 years?

A. $3,750
B. $5,600
C. $8,100
D. $15,000
E. $22,500


Kudos for a correct solution.


x=8%
112/x years=112/8=14 years
Now, money triples every 14 years
Therefore, in 14 yrs , if $2500 triples to $7500, in 28 years, it will again triple to $7500*3=$22,500
Answer E
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Re: Money invested at x%, compounded annually, triples in value in approxi  [#permalink]

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New post 27 Aug 2015, 20:25
112/8 = 14 years; 28/14= 2
therefor 2500 money triples in value every 2 years; therefore final value = 2500*3^2 = 22500
Hence answer is E
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Re: Money invested at x%, compounded annually, triples in value in approxi  [#permalink]

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New post 30 Aug 2015, 10:39
Bunuel wrote:
Money invested at x%, compounded annually, triples in value in approximately every 112/x years. If $2500 is invested at a rate of 8%, compounded annually, what will be its approximate worth in 28 years?

A. $3,750
B. $5,600
C. $8,100
D. $15,000
E. $22,500


Kudos for a correct solution.


GROCKIT OFFICIAL SOLUTION:

At first glance, this one seems pretty tricky because you are given x% as the interest rate and it asks you about compounding and it might seem difficult where to find a starting point for this. For this one, it might be a bit easier to think about this without the use of compound interest, which might unnecessarily confuse you. Here, we are given x% as 8%, so all we need to do is take 112/8 = 14. Thus, we know that the money triples in value every 14 years. Further, we know that the money will triple exactly twice in 28 years, once in 14 years and one more time at the 28th year. So first we need to multiply the original $2500 invested by 3 to get the balance at the end of year 14 (because it triples), to get $7,500 (or $2,500*3). Now, we know that this balance of $7,500 will triple again, so the final balance at the end of the next 14 year period will be $22,500 (or $7,500*3).

The correct answer choice is E.
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New to the Math Forum?
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Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


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Re: Money invested at x%, compounded annually, triples in value in approxi  [#permalink]

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