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# An amount is deposited into an account accruing interest ann

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VP
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An amount is deposited into an account accruing interest ann [#permalink]  26 Oct 2012, 23:54
00:00

Difficulty:

45% (medium)

Question Stats:

62% (03:50) correct 37% (02:36) wrong based on 58 sessions
An amount is deposited into an account accruing interest annually at a fixed percentage rate. It is valued at $900 in the third year (after interest has compounded twice), and$1080 in the fourth year (after interest has compounded three times). What is the original amount?

A. 520
B. 540
C. 600
D. 625
E. 650
[Reveal] Spoiler: OA
VP
Status: Final Lap Up!!!
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Kudos [?]: 208 [0], given: 65

Re: An amount is deposited into an account [#permalink]  26 Oct 2012, 23:56
correct me if i am wrong

R= 6/5

Now , 900 = P (1+x/100)^3

900 = P {6/5 *6/5 *6/5}

P = 521
Director
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Re: An amount is deposited into an account [#permalink]  27 Oct 2012, 00:03
1
KUDOS
Archit143 wrote:
correct me if i am wrong

R= 6/5

Now , 900 = P (1+x/100)^3

900 = P {6/5 *6/5 *6/5}

P = 521

Yup wrong approach.

if R is interest rate and P is original amount then from question :

900 = P (1+R/100)^2
and
1080 = P (1+R/100)^3

=> 1080/900 = 1+R/100
=> R = 20%

Substituting R in any one of the equations, you can obtain P. eg

900 = P (1+0.2)^2
=> P =625

Ans D it is.

Hope it helps.
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VP
Status: Final Lap Up!!!
Affiliations: NYK Line
Joined: 21 Sep 2012
Posts: 1078
Location: India
GMAT 1: 410 Q35 V11
GMAT 2: 530 Q44 V20
GMAT 3: 630 Q45 V31
GPA: 3.84
WE: Engineering (Transportation)
Followers: 25

Kudos [?]: 208 [0], given: 65

Re: An amount is deposited into an account [#permalink]  27 Oct 2012, 00:27
$900 in the third year t= 3 year .....why have you taken t= 2 years Director Status: Done with formalities.. and back.. Joined: 15 Sep 2012 Posts: 643 Location: India Concentration: Strategy, General Management Schools: Olin - Wash U - Class of 2015 WE: Information Technology (Computer Software) Followers: 32 Kudos [?]: 323 [1] , given: 23 Re: An amount is deposited into an account [#permalink] 27 Oct 2012, 00:44 1 This post received KUDOS Archit143 wrote:$900 in the third year

t= 3 year .....why have you taken t= 2 years

Question says in 3rd year, not after 3rd year. In 3rd year interest would have been compounded twice.
Hope it clarifies ur doubt.
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Re: An amount is deposited into an account [#permalink]  09 Dec 2013, 07:33
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Re: An amount is deposited into an account [#permalink]  19 Jan 2014, 00:42
Vips0000 wrote:
Archit143 wrote:
correct me if i am wrong

R= 6/5

Now , 900 = P (1+x/100)^3

900 = P {6/5 *6/5 *6/5}

P = 521

Yup wrong approach.

if R is interest rate and P is original amount then from question :

900 = P (1+R/100)^2
and
1080 = P (1+R/100)^3

=> 1080/900 = 1+R/100
=> R = 20%

Substituting R in any one of the equations, you can obtain P. eg

900 = P (1+0.2)^2
=> P =625

Ans D it is.

Hope it helps.

Am I missing anything ?
Compound interest formula is -> p(1+r/n)^(nt)
where t is time in years , r is the rate in decimal and n is the number of times interest is compounded in a year

based on this formula -> equation should be ->900 = p(1+r/2)^2
and ->1080 = p(1+r/3)^3

if these are the correct equations, how do we solve these 2 to get the correct value of P?
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Re: An amount is deposited into an account accruing interest ann [#permalink]  21 Jan 2014, 04:47
Interest rate: 1080/900 = 6/5 = 1.2

so you would have x * 1.2 * 1.2 = 900

900 / 1.2 = 750 (easy approach: 90/12 = 7.5) 2nd year
750 / 1.2 = 625 (same as above, make it easy: 75/12 = 6.25) 1st year.

Hence D!
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Re: An amount is deposited into an account accruing interest ann [#permalink]  22 Jan 2014, 01:51
unceldolan wrote:
Interest rate: 1080/900 = 6/5 = 1.2

so you would have x * 1.2 * 1.2 = 900

900 / 1.2 = 750 (easy approach: 90/12 = 7.5) 2nd year
750 / 1.2 = 625 (same as above, make it easy: 75/12 = 6.25) 1st year.

Hence D!

Sorry couldn't get you, can you elaborate?

Bunuel can you have a look at this? I believe vips0000 has some things missing in the equation,Thank you.
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Re: An amount is deposited into an account [#permalink]  22 Jan 2014, 02:13
1
KUDOS
Expert's post
stne wrote:
Vips0000 wrote:
Archit143 wrote:
An amount is deposited into an account accruing interest annually at a fixed percentage rate. It is valued at $900 in the third year (after interest has compounded twice), and$1080 in the fourth year (after interest has compounded three times). What is the original amount?

A. 520
B. 540
C. 600
D. 625
E. 650

correct me if i am wrong

R= 6/5

Now , 900 = P (1+x/100)^3

900 = P {6/5 *6/5 *6/5}

P = 521

Yup wrong approach.

if R is interest rate and P is original amount then from question :

900 = P (1+R/100)^2
and
1080 = P (1+R/100)^3

=> 1080/900 = 1+R/100
=> R = 20%

Substituting R in any one of the equations, you can obtain P. eg

900 = P (1+0.2)^2
=> P =625

Ans D it is.

Hope it helps.

Am I missing anything ?
Compound interest formula is -> p(1+r/n)^(nt)
where t is time in years , r is the rate in decimal and n is the number of times interest is compounded in a year

based on this formula -> equation should be ->900 = p(1+r/2)^2
and ->1080 = p(1+r/3)^3

if these are the correct equations, how do we solve these 2 to get the correct value of P?

The interest is compounded once a year. Why are you divide r by 2 and 3?

Vips0000 solution is 100% correct.

After interest has compounded twice the amount is 900: p(1+\frac{r}{100})^2=900.

After interest has compounded thrice the amount is 1,080: p(1+\frac{r}{100})^3=1,080.

Divide the second equation by the first one: 1+\frac{r}{100}=\frac{1,080}{900} --> 1+\frac{r}{100}=\frac{6}{5} --> r=20.

Substitute the value of r in either equations above: p(1+\frac{20}{100})^2=900 --> p=625.

Hope it's clear.
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Re: An amount is deposited into an account [#permalink]  22 Jan 2014, 02:41
Bunuel wrote:
stne wrote:
Am I missing anything ?
Compound interest formula is -> p(1+r/n)^(nt)
where t is time in years , r is the rate in decimal and n is the number of times interest is compounded in a year

based on this formula -> equation should be ->900 = p(1+r/2)^2
and ->1080 = p(1+r/3)^3

if these are the correct equations, how do we solve these 2 to get the correct value of P?

The interest is compounded once a year. Why are you divide r by 2 and 3?

Vips0000 solution is 100% correct.

After interest has compounded twice the amount is 900: p(1+\frac{r}{100})^2=900.

After interest has compounded thrice the amount is 1,080: p(1+\frac{r}{100})^3=1,080.

Divide the second equation by the first one: 1+\frac{r}{100}=\frac{1,080}{900} --> 1+\frac{r}{100}=\frac{6}{5} --> r=20.

Substitute the value of r in either equations above: p(1+\frac{20}{100})^2=900 --> p=625.

Hope it's clear.

oh I see !
When it said in the third year after interest was compounded twice , I thought in the third year interest was compounded twice , but that is not so.In this question interest is compounded annually.

Yes its clear now, thank you.
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Re: An amount is deposited into an account accruing interest ann [#permalink]  22 Jan 2014, 03:36
stne wrote:
unceldolan wrote:
Interest rate: 1080/900 = 6/5 = 1.2

so you would have x * 1.2 * 1.2 = 900

900 / 1.2 = 750 (easy approach: 90/12 = 7.5) 2nd year
750 / 1.2 = 625 (same as above, make it easy: 75/12 = 6.25) 1st year.

Hence D!

Sorry couldn't get you, can you elaborate?

Bunuel can you have a look at this? I believe vips0000 has some things missing in the equation,Thank you.

For interest problems you can either use the compound interest approach, as vips did, or my approach, repeating percentages.

First, you want to know the annual interest rate. As you yield 1080 in the 4th year and 900 in the third year, you have 900 * x = 1080. Hence 1080/900 = x = 1.2

This is our interest rate, our repeating percentage.

Thus, since we know that after the interest has compunded twice, the amount of the deposit is 900, we can say that

X (original amount) * 1.2 * 1.2 = 900.

You could compute and write 1.44x = 900 but in my opinion it is easier to divide 900 by 1.2 and the result by 1.2 again.

For my computing approach:

900/1.2 looks difficult at first. BUT you can simplify this by shifting the decimal point. E.g. 900/12 = something. still too difficult. Better: 90/12 = 7.5 But since you have shifted the decimal point in the numerator one to the left and the decimal point in the denominator one to the right you have to shift the decimal point in the result two to the right. hence 7.5 -> 75 -> 750.

Then you get x * 1.2 = 750 --> x = 750/1.2. Repeat the steps above and get X!

Hope it's clearer now!

Greets
Re: An amount is deposited into an account accruing interest ann   [#permalink] 22 Jan 2014, 03:36
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