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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]

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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. 100^4:105^4 E. 725:3225 [Reveal] Spoiler: OA _________________ Kudos will encourage many others, like me. Good Questions also deserve few KUDOS. Last edited by Bunuel on 28 Jan 2015, 07:43, edited 2 times in total. Edited the question. Kudos [?]: 1173 [7], given: 17 Math Expert Joined: 02 Sep 2009 Posts: 42264 Kudos [?]: 132745 [14], given: 12371 Re: A bank offers an interest of 5% per annum compounded annua [#permalink] ### Show Tags 11 Jun 2013, 05:59 14 This post received KUDOS Expert's post 16 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. _________________ Kudos [?]: 132745 [14], given: 12371 Manager Status: Working hard to score better on GMAT Joined: 02 Oct 2012 Posts: 89 Kudos [?]: 200 [0], given: 23 Location: Nepal Concentration: Finance, Entrepreneurship GPA: 3.83 WE: Accounting (Consulting) Re: A bank offers an interest of 5% per annum compounded annua [#permalink] ### Show Tags 14 Jun 2013, 03:22 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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Re: A bank offers an interest of 5% per annum compounded annua [#permalink]

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14 Jun 2013, 03:28
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 _________________ Kudos [?]: 132745 [0], given: 12371 Manager Joined: 29 Sep 2013 Posts: 51 Kudos [?]: 41 [3], given: 48 Re: A bank offers an interest of 5% per annum compounded annua [#permalink] ### Show Tags 26 Oct 2013, 02:14 3 This post received KUDOS 2 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

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

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Re: A bank offers an interest of 5% per annum compounded annua [#permalink]

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15 Apr 2014, 20:39
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? Kudos [?]: 13 [0], given: 19 SVP Status: The Best Or Nothing Joined: 27 Dec 2012 Posts: 1851 Kudos [?]: 2713 [0], given: 193 Location: India Concentration: General Management, Technology WE: Information Technology (Computer Software) Re: A bank offers an interest of 5% per annum compounded annua [#permalink] ### Show Tags 15 Apr 2014, 22:00 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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Re: A bank offers an interest of 5% per annum compounded annua [#permalink]

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15 Apr 2014, 22:06
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]

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03 Sep 2014, 21:59

10000*1.05^4/10000*1.05^5

we get 10000/10000*1.05=10000/10500=100/105

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Re: A bank offers an interest of 5% per annum compounded annua [#permalink]

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03 Sep 2014, 23:12
Temurkhon wrote:

10000*1.05^4/10000*1.05^5

we get 10000/10000*1.05=10000/10500=100/105

Hello.

You're correct for choosing C but wrong for interest formula buddy.

The question asks you to calculate ration of the interest earned in 4th year to the interest earned in 5th year. Your formula is to calculate Total value in 4th year and 5th year NOT interests.

In order to calculate INTEREST in 4th and 5th year, you have to calculate INTEREST in 1st year.

interest in 1st year = 10,000*0.05 = 500
interest in 2nd year = 500*1.05
interest in 3rd year = 500*1.05^2
interest in 4th year = 500*1.05^3
interest in 5th year = 500*1.05^4

Ratio = 1/1.05 = 100/105

Hope it helps.
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Re: A bank offers an interest of 5% per annum compounded annua [#permalink]

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07 Jul 2015, 11:40
Could somebody please explain, how interest could be calculated this way -

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 Since we are compounding, the interest for the second year should be 500 + 500*1.05 Kudos [?]: [0], given: 0 SVP Joined: 08 Jul 2010 Posts: 1847 Kudos [?]: 2343 [0], given: 51 Location: India GMAT: INSIGHT WE: Education (Education) Re: A bank offers an interest of 5% per annum compounded annua [#permalink] ### Show Tags 07 Jul 2015, 14:20 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. 100^4:105^4
E. 725:3225

Interest earned in the first year = $10,000 *(5/100) =$500
i.e. The interest earned in the 1st year = $500 The interest earned in the Second year =$10,000 *(5/100) + $500 *(5/100) =$500 + (5/100)*$500 =$500*1.05
i.e. The interest earned in the 2nd year = $500*1.05 Similarly, 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.

NOTE: Writing every step here is not a great idea as we must understand that Coumpound interest is a form of Geometric Progression in which the ratio of two consecutive terms remain constant hence

1st year interest / 2nd year interest = 2nd year interest / 3rd year interest = 3rd year interest / 4th year interest = 4th year interest / 5th year interest = 1/1.05

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Re: A bank offers an interest of 5% per annum compounded annua [#permalink]

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17 Sep 2015, 21:26
shankar245 wrote:
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? Hi Bunuel I'm agree with shankar245 the interest earned in the 4th years is= 10000(1+0.05)^4-10000=10000((1+0.05)^4-1) the interest earned in the 5th years is= 10000(1+0.05)^5-10000=10000((1+0.05)^5-1) the ratio is ((1+0.05)^4-1)/((1+0.05)^5-1)=0.78 can you please clarify? Kudos [?]: 1 [0], given: 60 SVP Joined: 08 Jul 2010 Posts: 1847 Kudos [?]: 2343 [0], given: 51 Location: India GMAT: INSIGHT WE: Education (Education) A bank offers an interest of 5% per annum compounded annua [#permalink] ### Show Tags 17 Sep 2015, 23:47 amirzohrevand wrote: shankar245 wrote: 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?

Hi Bunuel
I'm agree with shankar245
the interest earned in the 4th years is= 10000(1+0.05)^4-10000=10000((1+0.05)^4-1)
the interest earned in the 5th years is= 10000(1+0.05)^5-10000=10000((1+0.05)^5-1)
the ratio is ((1+0.05)^4-1)/((1+0.05)^5-1)=0.78

$500*1.05 = 500 + (5/100)*500 Where 500 is interest earned on principle And (5/100)*500 is interest earned on previous interest. So the expressions include both. I hope this helps! _________________ Prosper!!! GMATinsight Bhoopendra Singh and Dr.Sushma Jha e-mail: info@GMATinsight.com I Call us : +91-9999687183 / 9891333772 Online One-on-One Skype based classes and Classroom Coaching in South and West Delhi http://www.GMATinsight.com/testimonials.html 22 ONLINE FREE (FULL LENGTH) GMAT CAT (PRACTICE TESTS) LINK COLLECTION Last edited by GMATinsight on 18 Sep 2015, 04:06, edited 1 time in total. Kudos [?]: 2343 [0], given: 51 Intern Joined: 16 Aug 2013 Posts: 18 Kudos [?]: 1 [0], given: 60 A bank offers an interest of 5% per annum compounded annua [#permalink] ### Show Tags 18 Sep 2015, 01:06 Hi Bunuel I'm agree with shankar245 the interest earned in the 4th years is= 10000(1+0.05)^4-10000=10000((1+0.05)^4-1) the interest earned in the 5th years is= 10000(1+0.05)^5-10000=10000((1+0.05)^5-1) the ratio is ((1+0.05)^4-1)/((1+0.05)^5-1)=0.78 can you please clarify?[/quote]$50*1.05 = 50 + (5/100)*50

Where 50 is interest earned on principle
And

(5/100)*50 is interest earned on previous interest.

So the expressions include both.

I hope this helps![/quote]

Hi
Dear GMATinsight
I'm not agree with your approach cuz you dismissed the principle , however the principle must be seen.
your approach yields 0.92 but my approach yields 0.78
I'm still confused
could you elaborate more? plz
can you please let me know what is wrong with my approach?
tnx

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Re: A bank offers an interest of 5% per annum compounded annua [#permalink]

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18 Sep 2015, 04:04
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Expert's post
amirzohrevand wrote:

Hi
Dear GMATinsight
I'm not agree with your approach cuz you dismissed the principle , however the principle must be seen.
your approach yields 0.92 but my approach yields 0.78
I'm still confused
could you elaborate more? plz
can you please let me know what is wrong with my approach?
tnx

Principle = $10,000 Rate of Interest = 5% Interest earned in the first year =$10,000 *(5/100) = $500 i.e. The interest earned in the 1st year =$500

The interest earned in the Second year = $10,000 *(5/100) +$500 *(5/100) = $500 + (5/100)*$500 = $500*1.05 i.e. The interest earned in the 2nd year =$500*1.05
Similarly,
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. _________________ Prosper!!! GMATinsight Bhoopendra Singh and Dr.Sushma Jha e-mail: info@GMATinsight.com I Call us : +91-9999687183 / 9891333772 Online One-on-One Skype based classes and Classroom Coaching in South and West Delhi http://www.GMATinsight.com/testimonials.html 22 ONLINE FREE (FULL LENGTH) GMAT CAT (PRACTICE TESTS) LINK COLLECTION Kudos [?]: 2343 [1], given: 51 Current Student Joined: 04 May 2015 Posts: 74 Kudos [?]: 19 [0], given: 58 Concentration: Strategy, Operations WE: Operations (Military & Defense) Re: A bank offers an interest of 5% per annum compounded annua [#permalink] ### Show Tags 28 Sep 2015, 08:42 suk1234 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

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

I am literally ashamed that I didn't see this
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A bank offers an interest of 5% per annum compounded annua [#permalink]

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25 Apr 2016, 04:45
Quote:
amirzohrevand wrote:
Hi Bunuel
I'm agree with shankar245
the interest earned in the 4th years is= 10000(1+0.05)^4-10000=10000((1+0.05)^4-1)
the interest earned in the 5th years is= 10000(1+0.05)^5-10000=10000((1+0.05)^5-1)
the ratio is ((1+0.05)^4-1)/((1+0.05)^5-1)=0.78

\$50*1.05 = 50 + (5/100)*50

Where 50 is interest earned on principle
And

(5/100)*50 is interest earned on previous interest.

So the expressions include both.

I hope this helps!

Hi
Dear GMATinsight
I'm not agree with your approach cuz you dismissed the principle , however the principle must be seen.
your approach yields 0.92 but my approach yields 0.78
I'm still confused
could you elaborate more? plz
can you please let me know what is wrong with my approach?
tnx

Hi,

you are calculating total interest earned in 4 years i.e interest of 1year + 2year + 3year + 4year by that formula

Correct way to calculate 4th year interest is-

10,000(1 + .05)^4 - 10,000(1+ .05)^3

hope this helps!

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Re: A bank offers an interest of 5% per annum compounded annua [#permalink]

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10 Jul 2017, 19:18
C.I=P(1+r)^n
Interest earned in 4 th year = P(1+0.05)^3
Interest earned in 5 th year = P(1+0.05)^4
Ratio of Interest earned in 4 th year : Ratio of Interest earned in 5 th year = P(1+0.05)(1+0.05)(1+0.05)/P(1+0.05)(1+0.05)(1+0.05)(1+0.05)
=1/(1+0.05)
=100/105{Multiplied by 100}
Ans C

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

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20 Jul 2017, 22:27
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Bunuel or any mods,

Compound Interest (CI) for 1st year is $$\frac{5}{100}$$*10000 + 10000 = 10,500

Compound Interest (CI) for 2nd year is $$\frac{5}{100}$$*10500 + 10500 = 11,025

Compound Interest (CI) for 3rd year is $$\frac{5}{100}$$*11,025+ 11,025 ----- And this becomes an ugly math. Why? Where am I going wrong?

Compound Interest (CI) for 4th year is $$\frac{5}{100}$$*? + ? ------ By this point, I was heavily estimating the calculation. And I am still left with calculating for 5th year.

Compound Interest (CI) for 5th year is $$\frac{5}{100}$$*?+ ?

I somehow arrived at the correct answer but I see that there is inherently some mistake in my approach. Could someone help? TIA.

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