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DS - compound interest question

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msd_2008: Senior | Next Rank: 100 Posts; Posts: 66; Joined: Sun Jun 29, 2008 8:37 pm; Location: India; Thanked: 1 times

by msd_2008 » Sat Dec 06, 2008 1:55 am

Q. $10,000 is deposited in a certain account that pays r percent annual interest compounded annually, the amount D(t), in dollars, that the deposit will grow to in t years in given by D(t)=10,000(1+(r/100))t What amount will the deposit grow to in 3 years?

(1) D(t) = 11,000
(2) r=10

OA is D. But I disagree with it. Statement 1 gives me no info on 't' and 'r'....I only know the amount

Statement 2 gives me 'r'...but without the information on 't' its of no use. Thus statement 1 is also required to find out 't'
Hence I would choose C.
Can someone please explain whats wrong with my logic?

Regards
MSD

When the going gets tough, the tough gets going.

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Source: Beat The GMAT — Data Sufficiency | Sat Dec 06, 2008 1:55 am

parallel_chase: Legendary Member; Posts: 1153; Joined: Wed Jun 20, 2007 6:21 amFollowed by: 2 members; Thanked: 146 times

Re: DS - compound interest question

by parallel_chase » Sat Dec 06, 2008 4:36 am

msd_2008 wrote:Q. $10,000 is deposited in a certain account that pays r percent annual interest compounded annually, the amount D(t), in dollars, that the deposit will grow to in t years in given by D(t)=10,000(1+(r/100))t What amount will the deposit grow to in 3 years?

(1) D(t) = 11,000
(2) r=10

OA is D. But I disagree with it. Statement 1 gives me no info on 't' and 'r'....I only know the amount

Statement 2 gives me 'r'...but without the information on 't' its of no use. Thus statement 1 is also required to find out 't'
Hence I would choose C.
Can someone please explain whats wrong with my logic?

Regards
MSD

look closely the question stem gives you the value of t

t = 3

Hence D is correct.

Let me know if you have any doubts

No rest for the Wicked....

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msd_2008: Senior | Next Rank: 100 Posts; Posts: 66; Joined: Sun Jun 29, 2008 8:37 pm; Location: India; Thanked: 1 times

by msd_2008 » Sat Dec 06, 2008 4:44 am

Dear Friend,

How is t=3 and where is it given in the question?
Can you please help me understand ?

Regards
MSD

When the going gets tough, the tough gets going.

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parallel_chase: Legendary Member; Posts: 1153; Joined: Wed Jun 20, 2007 6:21 amFollowed by: 2 members; Thanked: 146 times

Re: DS - compound interest question

by parallel_chase » Sat Dec 06, 2008 5:00 am

D(t)=10,000(1+(r/100))t

Statement I

D(t) = 11000

d(1) = 11000

11000 = 10000(1+r/100)*1

11000/10000 = 1+r/100

11/10 -1 = r/100

1/10 = r/100

r = 10

D(t)=10,000(1+(r/100))t

substitute the value of r = 10

and calculate the value of t for 3 years

Statement II

You already have r = 10

t = 3

you can easily find the value of D(t)

Hope this helps.

No rest for the Wicked....

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cramya: Legendary Member; Posts: 2467; Joined: Thu Aug 28, 2008 6:14 pmFollowed by: 11 members; Thanked: 331 times

by cramya » Sat Dec 06, 2008 12:26 pm

Statement I

D(t) = 11000

d(1) = 11000

Parallel Chase,
I am missing something here.

How did u know t=1 for stmt I? Please help me understand.

Like MSD I was drawn to B) also.

Regards,
CR

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parallel_chase: Legendary Member; Posts: 1153; Joined: Wed Jun 20, 2007 6:21 amFollowed by: 2 members; Thanked: 146 times

by parallel_chase » Sat Dec 06, 2008 11:33 pm

cramya wrote:
Statement I

D(t) = 11000

d(1) = 11000

Parallel Chase,
I am missing something here.

How did u know t=1 for stmt I? Please help me understand.

Like MSD I was drawn to B) also.

Regards,
CR

The thing is if you take t=2, r will be negative, since we cannot have negative rates, only t=1 can be the possible value.

Let me if you have any other question.

No rest for the Wicked....

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mental: Master | Next Rank: 500 Posts; Posts: 145; Joined: Mon Sep 29, 2008 1:14 am; Thanked: 13 times

by mental » Wed Dec 10, 2008 3:29 am

The thing is if you take t=2, r will be negative, since we cannot have negative rates, only t=1 can be the possible value.

why?

lets take t=3

11000 = 10000{(1 + r/100)^3}

1.1 = (1 + r/100)^3

cube root of 1.1 is approximately 1.03

1.03 = 1 + r/100

r = 3%

you have already shown with t = 1, r=10%

why t=2 gives a negetive ans?

11000 = 10000{(1 + r/100)^2}
1.1 = (1 + r/100)^2
square root of 1.1 is approximately 1.05
1.05 = 1 + r/100
r = 5%

different values of r

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Stuart@KaplanGMAT: GMAT Instructor; Posts: 3225; Joined: Tue Jan 08, 2008 2:40 pmFollowed by: 614 members; Location: Toronto; Thanked: 1710 times; GMAT Score:800

by Stuart@KaplanGMAT » Wed Dec 10, 2008 10:51 am

I posted my thoughts here:

https://www.beatthegmat.com/compound-int ... 19026.html

Statement (1) is sufficient as written, but makes no sense - it basically says that D(t) has a fixed value regardless of the time period. So, the answer to the question would be "$11000".

It really should read D(1) = 11000.

Has anyone checked for tyops?

Stuart Kovinsky | Kaplan GMAT Faculty | Toronto

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ronniecoleman: Legendary Member; Posts: 546; Joined: Sun Nov 16, 2008 11:00 pm; Location: New Delhi , India; Thanked: 13 times

by ronniecoleman » Fri Dec 12, 2008 3:41 am

quality is the key guys/gals!!

please verify the source!

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revoltangel: Junior | Next Rank: 30 Posts; Posts: 23; Joined: Wed Oct 15, 2008 10:11 am; Location: california

by revoltangel » Wed Dec 31, 2008 1:05 pm

msd_2008 wrote:Dear Friend,

How is t=3 and where is it given in the question?
Can you please help me understand ?

Regards
MSD

The last sentence asks how much you will get in 3 years. Therefore, t=3.

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sellaia: Newbie | Next Rank: 10 Posts; Posts: 4; Joined: Sat Nov 26, 2011 1:17 pm

by sellaia » Fri Dec 16, 2011 8:15 pm

Stuart Kovinsky wrote:I posted my thoughts here:

https://www.beatthegmat.com/compound-int ... 19026.html

Statement (1) is sufficient as written, but makes no sense - it basically says that D(t) has a fixed value regardless of the time period. So, the answer to the question would be "$11000".

It really should read D(1) = 11000.

Has anyone checked for tyops?

Thanks that's really what confused me. Also, I didn't understand how the t in D(t) translated into a one within the equality D(t) =11,000 = 10,000(1+r/100)^1

Also, can I ask you where are those questions from ?

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