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# A bank offers an interest of 5% per annum compounded annua

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A bank offers an interest of 5% per annum compounded annua [#permalink]  11 Jun 2013, 02:58
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A bank offers an interest of 5% per annum compounded annually on all its deposits. If $10,000 is deposited, what will be the ratio of the interest earned in the 4th year to the interest earned in the 5th year? A. 1:5 B. 625:3125 C. 100:105 D. 1004:1054 E. 725:3225 [Reveal] Spoiler: OA _________________ Kudos will encourage many others, like me. Good Questions also deserve few KUDOS. Last edited by Bunuel on 11 Jun 2013, 04:46, edited 1 time in total. Edited the question. Math Expert Joined: 02 Sep 2009 Posts: 18676 Followers: 3229 Kudos [?]: 22151 [2] , given: 2599 Re: A bank offers an interest of 5% per annum compounded annua [#permalink] 11 Jun 2013, 04:59 2 This post received KUDOS Expert's post 1 This post was BOOKMARKED emmak wrote: A bank offers an interest of 5% per annum compounded annually on all its deposits. If$10,000 is deposited, what will be the ratio of the interest earned in the 4th year to the interest earned in the 5th year?

A. 1:5
B. 625:3125
C. 100:105
D. 1004:1054
E. 725:3225

The interest earned in the 1st year = $500 The interest earned in the 2nd year =$500*1.05
The interest earned in the 3rd year = $500*1.05^2 The interest earned in the 4th year =$500*1.05^3
The interest earned in the 5th year = $500*1.05^4 (500*1.05^3)/(500*1.05^4) = 1/1.05=100/105. Answer: C. _________________ Manager Status: Working hard to score better on GMAT Joined: 02 Oct 2012 Posts: 92 Location: Nepal Concentration: Finance, Entrepreneurship GPA: 3.83 WE: Accounting (Consulting) Followers: 0 Kudos [?]: 40 [0], given: 23 Re: A bank offers an interest of 5% per annum compounded annua [#permalink] 14 Jun 2013, 02:22 emmak wrote: A bank offers an interest of 5% per annum compounded annually on all its deposits. If$10,000 is deposited, what will be the ratio of the interest earned in the 4th year to the interest earned in the 5th year?

A. 1:5
B. 625:3125
C. 100:105
D. 1004:1054
E. 725:3225

Hi Bunuel,
Here is my approach: is this correct?

Interest earned in 4 year= 10000(1+0.05)^4

Interest earned in 5 year= 10000(1+0.05)^5

Ratio= {10000(1.05)^4}/{10000(1.05^5)} =>1.05^4/1.05^5 =>1/1.05 Multiplied by 100 in both numerator and denominator gives 100:105

Hence Ans:C
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Math Expert
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Re: A bank offers an interest of 5% per annum compounded annua [#permalink]  14 Jun 2013, 02:28
Expert's post
atalpanditgmat wrote:
emmak wrote:
A bank offers an interest of 5% per annum compounded annually on all its deposits. If $10,000 is deposited, what will be the ratio of the interest earned in the 4th year to the interest earned in the 5th year? A. 1:5 B. 625:3125 C. 100:105 D. 1004:1054 E. 725:3225 Hi Bunuel, Here is my approach: is this correct? Interest earned in 4 year= 10000(1+0.05)^4 Interest earned in 5 year= 10000(1+0.05)^5 Ratio= {10000(1.05)^4}/{10000(1.05^5)} =>1.05^4/1.05^5 =>1/1.05 Multiplied by 100 in both numerator and denominator gives 100:105 Hence Ans:C Check here: a-bank-offers-an-interest-of-5-per-annum-compounded-annua-154203.html#p1234708 _________________ Intern Joined: 29 Sep 2013 Posts: 46 Followers: 0 Kudos [?]: 11 [0], given: 35 Re: A bank offers an interest of 5% per annum compounded annua [#permalink] 26 Oct 2013, 01:14 emmak wrote: A bank offers an interest of 5% per annum compounded annually on all its deposits. If$10,000 is deposited, what will be the ratio of the interest earned in the 4th year to the interest earned in the 5th year?

A. 1:5
B. 625:3125
C. 100:105
D. 1004:1054
E. 725:3225

Thirty seconds approach, regardless of what the figure is at the 4th year it will at act as a base figure (100) for the next years 5% increase (to 105). So the ratio is 100:105 or option C
Manager
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Re: A bank offers an interest of 5% per annum compounded annua [#permalink]  15 Apr 2014, 19:39
Buneul,

I have a doubt.

Quote:
The interest earned in the 1st year = $50 The interest earned in the 2nd year =$50*1.05
The interest earned in the 3rd year = $50*1.05^2 The interest earned in the 4th year =$50*1.05^3
The interest earned in the 5th year = $50*1.05^4 So we are just calculating the interest from interest.Are we not supposed to calculate the interest from the principle amount every year? Director Status: The Best Or Nothing Joined: 27 Dec 2012 Posts: 634 Location: India Concentration: General Management, Technology WE: Information Technology (Computer Software) Followers: 2 Kudos [?]: 144 [0], given: 161 Re: A bank offers an interest of 5% per annum compounded annua [#permalink] 15 Apr 2014, 21:00 atalpanditgmat wrote: emmak wrote: A bank offers an interest of 5% per annum compounded annually on all its deposits. If$10,000 is deposited, what will be the ratio of the interest earned in the 4th year to the interest earned in the 5th year?

A. 1:5
B. 625:3125
C. 100:105
D. 1004:1054
E. 725:3225

Hi Bunuel,
Here is my approach: is this correct?

Interest earned in 4 year= 10000(1+0.05)^4

Interest earned in 5 year= 10000(1+0.05)^5

Ratio= {10000(1.05)^4}/{10000(1.05^5)} =>1.05^4/1.05^5 =>1/1.05 Multiplied by 100 in both numerator and denominator gives 100:105

Hence Ans:C

This formula is to calculate the total amount, not the compound interest

You require to subtract the Principal to get the resultant compound interest

We require to calculate ratio of interest earned in 4th & 5th year

This method you're using is calculating ratio of 4 yr deposit to 5 yr deposit
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Director
Status: The Best Or Nothing
Joined: 27 Dec 2012
Posts: 634
Location: India
Concentration: General Management, Technology
WE: Information Technology (Computer Software)
Followers: 2

Kudos [?]: 144 [0], given: 161

Re: A bank offers an interest of 5% per annum compounded annua [#permalink]  15 Apr 2014, 21:06
Bunuel wrote:
emmak wrote:
A bank offers an interest of 5% per annum compounded annually on all its deposits. If $10,000 is deposited, what will be the ratio of the interest earned in the 4th year to the interest earned in the 5th year? A. 1:5 B. 625:3125 C. 100:105 D. 1004:1054 E. 725:3225 The interest earned in the 1st year =$50
The interest earned in the 2nd year = $50*1.05 The interest earned in the 3rd year =$50*1.05^2
The interest earned in the 4th year = $50*1.05^3 The interest earned in the 5th year =$50*1.05^4

(50*1.05^3)/(50*1.05^4) = 1/1.05=100/105.

Bunuel, can you please correct this?

It should be 500

\frac{10000 * 5 * 1}{100} = 500
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Re: A bank offers an interest of 5% per annum compounded annua   [#permalink] 15 Apr 2014, 21:06
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