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# A certain sum amount to $1400 in 2 yrs and$2000 in five years on cert

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Manager
Joined: 06 Apr 2010
Posts: 117
A certain sum amount to $1400 in 2 yrs and$2000 in five years on cert  [#permalink]

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31 Oct 2010, 04:34
2
00:00

Difficulty:

35% (medium)

Question Stats:

72% (02:13) correct 28% (02:47) wrong based on 46 sessions

A certain sum amount to $1400 in 2 yrs and$2000 in five years on certain fixed simple interest. In how many yrs would the amount be $1440 had it been put at the rate of interest compounded annually? 1. 4.5 2. 3.5 3. 3 4. 2 5. 1 Veritas Prep GMAT Instructor Joined: 16 Oct 2010 Posts: 8558 Location: Pune, India Re: A certain sum amount to$1400 in 2 yrs and $2000 in five years on cert [#permalink] ### Show Tags 31 Oct 2010, 05:45 1 1 The sum amounts to 1400 in 2 yrs and 2000 in 5 yrs. It increases by 600 in 3 yrs. Since simple interest remains the same every year, SI = 200. Then the original sum must have been 1400 - 400 = 1000 and rate of interest must have been 20%. If compounded annually, a sum of 1000 at 20% will become a little more than 1200 in 1 year, more than 1400 in 2 yrs and more than 1600 in 3 yrs... Answer must be 2 yrs. Note: Even these calculations are excess. At SI, if sum is 1400 in 2 years, same sum at same rate of interest will become something more than 1400 in 2 yrs and more than 1600 in 3 years. The only option that fits is 2 yrs. _________________ Karishma Veritas Prep GMAT Instructor Learn more about how Veritas Prep can help you achieve a great GMAT score by checking out their GMAT Prep Options > GMAT self-study has never been more personalized or more fun. Try ORION Free! Manager Joined: 09 Jun 2010 Posts: 103 Re: A certain sum amount to$1400 in 2 yrs and $2000 in five years on cert [#permalink] ### Show Tags 31 Oct 2010, 07:25 We can form equations as following: Initial amount = P, Total amount after interest = T, Interest per year = I T = P+I Given T1 = P+2I = 1400 & T2 = P+ 5I = 2000 From this we get, P = 1000 & I = 200$

Now we know that simple interest is < Compound interest ( CI = SI only after 1st year if CI is compounded annually)

consider simple interest - after 1st yer it is 200$, after 2nd years it is 400$ and after 3rd year it is 600$. To get a 440$ compound interest the duration have to be > 1 year and < 3 years.

Only option fitting : Option D.
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Joined: 22 May 2016
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A certain sum amount to $1400 in 2 yrs and$2000 in five years on cert  [#permalink]

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20 Nov 2017, 12:26
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1
udaymathapati wrote:
A certain sum amount to $1400 in 2 yrs and$2000 in five years on certain fixed simple interest. In how many yrs would the amount be $1440 had it been put at the rate of interest compounded annually? 1. 4.5 2. 3.5 3. 3 4. 2 5. 1 Simple interest, SI, per year Years (5-2) = (2,000-1,400) =$600 SI in 3 years
SI per year is $600/3 =$200

Original amount?
Year 2 - 2(200): 1,400- 2(200) = $1,000 Simple interest rate:$$\frac{200}{1000} *100$$ = 20% How many years for$1,000 to be $1,440 if interest rate were compounded annually? First year only: simple interest = interest compounded annually End Year 1: (1,000 + 200) =$1,200

End Year 2: (1,200 * 1.2) = $1,440 OR 1,200+(.2)(1,200)=(1,200+240)=$1,440

Alternatively,
$$A = P(1 + r)^{t}$$
P = principal, r = decimal interest rate, t = time

The number "$1,440," and compound interest rate "1.2" are big hints. $$(1.2)^2 = 1.44$$; principal =$1,000

Mentally I just did
$$1,000(1.2)^2 = 1,000(1.44) = 1,440$$

The long way:

$$1,440 = 1,000(1 + .20)^{x}$$
$$1,440 = 1,000(1.20)^{x}$$
$$\frac{1,440}{1,000} = (1.2)^{x}$$
$$1.44 = 1.2^{x}$$
$$(1.2)^1(1.2)^1 = 1.2^{x}$$
$$1 + 1 = x$$
$$x = 2$$

A certain sum amount to $1400 in 2 yrs and$2000 in five years on cert &nbs [#permalink] 20 Nov 2017, 12:26
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