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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] New post 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

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Last edited by Bunuel on 11 Jun 2013, 04:46, edited 1 time in total.
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Re: A bank offers an interest of 5% per annum compounded annua [#permalink] New post 11 Jun 2013, 04:59
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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.
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Re: A bank offers an interest of 5% per annum compounded annua [#permalink] New post 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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Re: A bank offers an interest of 5% per annum compounded annua [#permalink] New post 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
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Re: A bank offers an interest of 5% per annum compounded annua [#permalink] New post 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
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Re: A bank offers an interest of 5% per annum compounded annua [#permalink] New post 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?
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Re: A bank offers an interest of 5% per annum compounded annua [#permalink] New post 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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Re: A bank offers an interest of 5% per annum compounded annua [#permalink] New post 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.

Answer: C.



Bunuel, can you please correct this?

It should be 500

\frac{10000 * 5 * 1}{100} = 500
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Bank Interest Question [#permalink] New post 23 Jul 2014, 08:42
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 : 100^5
e) 725 : 3225


First year: 10,000+5
NOTE: Using fractions is typically the easiest way to calculate, so we’ll represent 5% as 1/20 from here on out.

Second year: 10,000∗21/20+1/20∗(10,000∗21/20)=21/20(10,000∗21/20)=(21/20)2∗10,000
Third year: (21/20)2(10,000)+1/20∗(21/20)2(10,000)=21/20∗(21/20)2(10,000)=(21/20)3∗10,000)
If you follow the pattern, the total value at the end of each year will simply be (21/20)n(10,000) at the end of the nth year. The amount of interest each year is 1/20 of the previous year’s balance (that …+1/20 * the previous year). So, the amount of interest calculated in the 4th year will be:

1/20∗(21/20)3(10,000)
And the amount of interest earned in the 5th year will be:

1/20∗(21/20)4(10,000)
Putting those into ratio, you’ll see that the 1/20 and the 10,000 is common to both, so those terms divide out, leaving simply:

(21/20)3/(21/20)4
Factoring out the common (21/20)3 term, we’re left with 1/(21/20). Dividing by a fraction is the same as multiplying by the reciprocal, so that can be expressed as 20/21, which is the same as 100/105.


MY CONFUSION : IT WAS A LONG WORDY EXPLANATION, AND I GOT LOST IN IT, SO I NEED A MORE CONCISE EXPLANATION IF POSSIBLE, ALSO WHERE DOES THE 21/ 20 COME FROM? IN SECOND YEAR HOW COME WE ARE ADDING 21/20 AND 1/20 AND THEN MULTIPLYING BY 10,000 AND 1/20 WHY NOT MULTIPLY BY 21/20?
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Re: A bank offers an interest of 5% per annum compounded annua [#permalink] New post 23 Jul 2014, 08:47
Expert's post
sagnik2422 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 : 100^5
e) 725 : 3225


First year: 10,000+5
NOTE: Using fractions is typically the easiest way to calculate, so we’ll represent 5% as 1/20 from here on out.

Second year: 10,000∗21/20+1/20∗(10,000∗21/20)=21/20(10,000∗21/20)=(21/20)2∗10,000
Third year: (21/20)2(10,000)+1/20∗(21/20)2(10,000)=21/20∗(21/20)2(10,000)=(21/20)3∗10,000)
If you follow the pattern, the total value at the end of each year will simply be (21/20)n(10,000) at the end of the nth year. The amount of interest each year is 1/20 of the previous year’s balance (that …+1/20 * the previous year). So, the amount of interest calculated in the 4th year will be:

1/20∗(21/20)3(10,000)
And the amount of interest earned in the 5th year will be:

1/20∗(21/20)4(10,000)
Putting those into ratio, you’ll see that the 1/20 and the 10,000 is common to both, so those terms divide out, leaving simply:

(21/20)3/(21/20)4
Factoring out the common (21/20)3 term, we’re left with 1/(21/20). Dividing by a fraction is the same as multiplying by the reciprocal, so that can be expressed as 20/21, which is the same as 100/105.


MY CONFUSION : IT WAS A LONG WORDY EXPLANATION, AND I GOT LOST IN IT, SO I NEED A MORE CONCISE EXPLANATION IF POSSIBLE, ALSO WHERE DOES THE 21/ 20 COME FROM? IN SECOND YEAR HOW COME WE ARE ADDING 21/20 AND 1/20 AND THEN MULTIPLYING BY 10,000 AND 1/20 WHY NOT MULTIPLY BY 21/20?


Merging topics. Please refer to the discussion above.

P.S. Please read carefully and follow: rules-for-posting-please-read-this-before-posting-133935.html Pay attention to rules 1 and 3. Thank you.


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Re: A bank offers an interest of 5% per annum compounded annua   [#permalink] 23 Jul 2014, 08:47
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