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08 Aug 2022, 01:30
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D
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Difficulty:
25%
(medium)
Question Stats:
78% (01:33) correct
22%
(01:54)
wrong
based on 143
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A sum of money is invested under compound interest for a few years. After how many years will the sum of money become nine times its present value?
(1) The sum of money invested under compound interest at the same rate of interest per annum became thrice its value in 6 years.
(2) The sum of money, under compound interest, at the same rate of interest per annum, would become twenty-seven times its present value in 9 years.
(1) The sum of money invested under compound interest at the same rate of interest per annum became thrice its value in 6 years.
(2) The sum of money, under compound interest, at the same rate of interest per annum, would become twenty-seven times its present value in 9 years.
08 Aug 2022, 05:10
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CASE I:
Final amount = 3x Initial Amount
A=P(1+r/n)^nt
3P=P(1+r/n)^6t
3=(1+r/n)^6t
Squaring both sides, we get
9=(1+r/n)^12t
which is what we need; money will be 9 times in 12 years
Eliminate BCE
Case II
Similarly
27=(1+r/n)^9t
Raising both sides by 2/3 power
9=(1+r/n)^6t
which is what we need; money will be 9 times in 6 years
Eliminate A
Answer D
Final amount = 3x Initial Amount
A=P(1+r/n)^nt
3P=P(1+r/n)^6t
3=(1+r/n)^6t
Squaring both sides, we get
9=(1+r/n)^12t
which is what we need; money will be 9 times in 12 years
Eliminate BCE
Case II
Similarly
27=(1+r/n)^9t
Raising both sides by 2/3 power
9=(1+r/n)^6t
which is what we need; money will be 9 times in 6 years
Eliminate A
Answer D
22 Aug 2022, 11:07
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VenDeTa796
Interesting that the question is set up to have two different values for each statement (even though each is sufficient)
Answer is D.
S1
Say the starting amount = $100
We want to know how many years it takes for the starting amount to become 9 times itself.
We are told in s1 that the starting amount triples in 6 years.
$100 ——————(6 yr) ——————-> $300
Percentage increase of 200% or 3 times the original
The percentage increase is constant over a certain time period under compound interest (whereas under simple internet there is a constant incremental change). The percentage increase is continually applied to the new amount, not initial amount.
After 6 years we have $300 in our account
In another 6 years, the amount will increase by 200% again
$300 —————(12 total years) ———-> $900
$900 in the account is 9 TIMES the original
It would thus take 12 years
S1 is sufficient alone
Stmt. 2:
Under compound interest, the starting amount will increase at a certain percentage for a fixed time period.
Assume we start with $100. The final amount after 9 years is 27 times the original, or $2,700.
If we keep tripling the starting sum (i.e., the constant factor is 3 times the amount int he account every X years), we will reach $2,700 after 3 time periods of X years
$100 ———(x years) ———->$300 —————(+ another x years)——-> $900 ————— (+ another x years)———> $2,700
Since it takes a total of 9 years for the amount to become 27 times the starting value (i.e., $2700)
(x) + (x) + (x) = 9 years
3(x) = 9 years
(x) = 3 years
Over a 3 year period ———> the starting amount of $100 will be 3 times itself —- or $300
Over another 3 year period (for a total of 6 years) the amount will become 3 times the $300 in the account —- or $900
which is 9 times the starting amount of $100
Answer: T = 6 years for the starting amount to become 9 times itself
S2 sufficient also
*D*
Edit: apologies, I clicked on the wrong post. I intended to click on “reply to question”, not reply to the above post.
Posted from my mobile device
