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Updated on: 28 Jan 2013, 09:14
1
KUDOS
3
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Difficulty:

5% (low)

Question Stats:

95% (00:37) correct 5% (00:54) wrong based on 282 sessions

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Two years ago, Sam put $1,000 into a savings account. At the end of the first year, his account had accrued$100 in interest bringing his total balance to $1,100. The next year, his account balance increased by 10%. At the end of the two years, by what percent has Sam's account balance increased from his initial deposit of$1,000 ?

A. 19%
B. 20%
C. 21%
D. 22%
E. 25%
[Reveal] Spoiler: OA

_________________

KUDOS is the good manner to help the entire community.

Originally posted by Rock750 on 19 Jan 2013, 08:05.
Last edited by Rock750 on 28 Jan 2013, 09:14, edited 1 time in total.
Intern
Joined: 16 Nov 2012
Posts: 32
Location: United States
Concentration: Operations, Social Entrepreneurship
Schools: ISB '15, NUS '16
GMAT Date: 08-27-2013
GPA: 3.46
WE: Project Management (Other)

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29 Nov 2013, 04:06
%-change = change in value / original value

original value here: 1000 $change value: we need to calculate the account after year 2. we take our 1100$ after 1 year and calculate 10 % which is 110 $. we get 1210$ after 2 years. hence there was a change in value of 210 $. plug into formula : 210$ / 1000 $= 21 / 100 =21 % Thus C. Hope it helps. SC Moderator Joined: 22 May 2016 Posts: 1554 Two years ago, Sam put$1,000 into a savings account. [#permalink]

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19 Jul 2017, 14:34
Rock750 wrote:
Two years ago, Sam put $1,000 into a savings account. At the end of the first year, his account had accrued$100 in interest bringing his total balance to $1,100. The next year, his account balance increased by 10%. At the end of the two years, by what percent has Sam's account balance increased from his initial deposit of$1,000 ?

A. 19%
B. 20%
C. 21%
D. 22%
E. 25%

Year 1 interest: $100 Year 2 interest, 10% of 1,100 =$110

Total interest = 100 + 110 = $210 (which equals the change in value) $$\frac{change}{original}$$ x 100 = percent change $$\frac{210}{1000}$$ = .21 x 100 = 21% Answer C _________________ At the still point, there the dance is. -- T.S. Eliot Formerly genxer123 Study Buddy Forum Moderator Joined: 04 Sep 2016 Posts: 888 Location: India WE: Engineering (Other) Two years ago, Sam put$1,000 into a savings account. [#permalink]

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05 Apr 2018, 18:51
generis

Quote:
Two years ago, Sam put $1,000 into a savings account. At the end of the first year, his account had accrued$100 in interest bringing his total balance to $1,100. The next year, his account balance increased by 10%. At the end of the two years, by what percent has Sam's account balance increased from his initial deposit of$1,000 ?

A. 19%
B. 20%
C. 21%
D. 22%
E. 25%

Quote:
Year 1 interest: $100 Year 2 interest, 10% of 1,100 =$110

Total interest = 100 + 110 = $210 (which equals the change in value) $$\frac{change}{original}$$ x 100 = percent change $$\frac{210}{1000}$$ = .21 x 100 = 21% Answer C We are not given rate of interest (r) directly. Did you calculate the same by knowing principal amount (Rs.1000), tenure (1 year), interest (Rs. 100) and using equation: Interest = PrT/100 for the first year and then using the same for the second year? niks18 Is the highlighted part in question required to be given? _________________ It's the journey that brings us happiness not the destination. SC Moderator Joined: 22 May 2016 Posts: 1554 Two years ago, Sam put$1,000 into a savings account. [#permalink]

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06 Apr 2018, 13:30
generis
Quote:
Two years ago, Sam put $1,000 into a savings account. At the end of the first year, his account had accrued$100 in interest bringing his total balance to $1,100. The next year, his account balance increased by 10%. At the end of the two years, by what percent has Sam's account balance increased from his initial deposit of$1,000 ?

A. 19%
B. 20%
C. 21%
D. 22%
E. 25%

Quote:
Year 1 interest: $100 Year 2 interest, 10% of 1,100 =$110

Total interest = 100 + 110 = $210 (which equals the change in value) $$\frac{change}{original}$$ x 100 = percent change $$\frac{210}{1000}$$ = .21 x 100 = 21% Answer C We are not given rate of interest (r) directly. Did you calculate the same by knowing principal amount (Rs.1000), tenure (1 year), interest (Rs. 100) and using equation: Interest = PrT/100 for the first year and then using the same for the second year? niks18 Is the highlighted part in question required to be given? adkikani , I think you ask two questions. 1) did I use simple interest rate equation? 2) why does it look as if I did? No, I did not use interest rate I used net change in money amount for each year Year 1's change amount is given: +$100
Year 2's change rate is given:
10% increase on $1,100 = +$110

Then I calculated percent change from net amount change,
see original post. (Change/Original * 100)

is interesting.

If Sam left the earned interest in the bank;
and if Sam left the account alone;
of course we can calculate the amount in the account.
He put in $1000. He earned$100. His total = $1,100. But we don't know what Sam did with the account. The highlighted portion tells us that he left it alone. • I suspect it appears that I used interest rates because for any given first year, if simple interest rate = annual compound interest rate, amount yielded is identical. Use interest rate? Yes, but . . . If I were to calculate percent increase using interest rates, I would: 1) not use strict SI (it's inaccurate)* 2) use multipliers or 3) use compound annual interest For #2 and #3, I would omit principal amount. Not needed. Percent change using multipliers= compound interest rate Multipliers - TOTAL factor increase Multiplier, Year 1? Deduce from base + interest $$1,000 + 100 = 1,100$$ Multiplier: $$\frac{1,100}{1,000}= 1.1$$ Multiplier for Year 2? Given. 10% increase on extant amount = $$1.1$$ Multipliers: TOTAL increase factor? (Year 1 multiplier * Year 2 multiplier) = total increase factor Total increase factor: $$(1.1 * 1.1) = 1.21$$ Original base? $$1$$ Compound annual interest: TOTAL factor increase $$A_{final}=P(1+.10)^{nt}$$ $$A_{final}=P(1.1)^{1*2}$$ $$A_{final}=P(1.1)^2$$ $$A_{final}=1.21P$$ $$A_{original}= P$$ Percent increase: $$\frac{New-Old}{Old}*100$$ $$(\frac{1.21-1}{1}*100)=(\frac{.21}{1}*100)$$ $$= .21*100=21$$ percent OR $$(\frac{1.21P-1P}{1P}*100)=(\frac{.21P}{1P}*100)$$ $$=.21*100=21$$ percent Hope that answers your question. *SI amount for both years? INCORRECT if years are taken together Run this formula for SI: $$A_{final} = P(1 + rt)$$ Total after two years is$1,200. Not correct.

If you separate Year 1 and Year 2;
change $$P$$ from $1,000 to$1,100;
and change $$t$$ from 2 to 1;
SI formula will work.

_________________

At the still point, there the dance is. -- T.S. Eliot
Formerly genxer123