Compound interest & donald's plans

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bhumika.k.shah: Legendary Member; Posts: 941; Joined: Sun Dec 27, 2009 12:28 am; Thanked: 20 times; Followed by:1 members

Compound interest & donald's plans

by bhumika.k.shah » Mon Feb 15, 2010 9:36 am

Donald plans to invest x dollars in a savings account that pays interest at an annual rate of 8% compounded quarterly. Approximately what amount is the minimum that Donald will need to invest to earn over $100 in interest within 6 months?

A .$1500
B. $1750
C. $2000
D. $2500
E. $3000

If its compounded quaterly = 3 months ...then shouldnt it be 16% for 6 months ?

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Source: Beat The GMAT — Problem Solving | Mon Feb 15, 2010 9:36 am

shashank.ism: Legendary Member; Posts: 1022; Joined: Mon Jul 20, 2009 11:49 pm; Location: Gandhinagar; Thanked: 41 times; Followed by:2 members

by shashank.ism » Mon Feb 15, 2010 9:43 am

bhumika.k.shah wrote:Donald plans to invest x dollars in a savings account that pays interest at an annual rate of 8% compounded quarterly. Approximately what amount is the minimum that Donald will need to invest to earn over $100 in interest within 6 months?

A .$1500
B. $1750
C. $2000
D. $2500
E. $3000

If its compounded quaterly = 3 months ...then shouldnt it be 16% for 6 months ?

100 + P = P (1 + 2/100)^ 2

2/100 because we are given 8% annual rate and since compounded quarterly,
quarterly rate=2%
Since problem is seeking 100$ compound interest in 6 months, which is 2 quarters
you raise (1 + RT/100) portion by power of 2.

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ajith: Legendary Member; Posts: 1275; Joined: Thu Sep 21, 2006 11:13 pm; Location: Arabian Sea; Thanked: 125 times; Followed by:2 members

by ajith » Mon Feb 15, 2010 10:16 am

bhumika.k.shah wrote:Donald plans to invest x dollars in a savings account that pays interest at an annual rate of 8% compounded quarterly. Approximately what amount is the minimum that Donald will need to invest to earn over $100 in interest within 6 months?

A .$1500
B. $1750
C. $2000
D. $2500
E. $3000

If its compounded quaterly = 3 months ...then shouldnt it be 16% for 6 months ?

annual rate of 8% compounded quarterly. It is expressed as an annual rate not as quarterly rate. We have to find the quarterly rate by dividing the annual rate by 4

Annual rate is 8%
Quarterly rate as shashank has rightly pointed out is 2% (8/4)

Say the amount required to get 100 Dollar interest is X

X(1+2/100)^2 - X = 100

X(1 + 0.02)^2 - X = 100

X(1+ 2*0.02+ 0.0004) - X = 100
0.0404 X = 100
X = 2500 [ 100/0.04]

Always borrow money from a pessimist, he doesn't expect to be paid back.

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komal: Legendary Member; Posts: 777; Joined: Fri Jan 01, 2010 4:02 am; Location: Mumbai, India; Thanked: 117 times; Followed by:47 members

by komal » Tue Feb 16, 2010 8:35 am

bhumika.k.shah wrote:Donald plans to invest x dollars in a savings account that pays interest at an annual rate of 8% compounded quarterly. Approximately what amount is the minimum that Donald will need to invest to earn over $100 in interest within 6 months?

A .$1500
B. $1750
C. $2000
D. $2500
E. $3000

If its compounded quaterly = 3 months ...then shouldnt it be 16% for 6 months ?

Compound interest formula

A = P ( 1+r/n)power nt

given, n= 4 (quaterly);r =.08

the approach is substitution,

our interest requirement is 100$ after 6 months, 2 compounding period. interest per compounding period is 2%

lets take 1500, after 3 months interest accumulated is 30$, total amount is 1530
after 6 months, interest is 30.6$ and total is 1560.6$, so not 1500

1500 & 1750 have a difference of 250$ only , but the expected interest different is around 40$ hence you can straightaway rule out 1750

2000 is again can be ruled out as approx 4% interest yeilds only 80$

2500$ is a good bet, first 3 months it earns 50$ as interest, next 3 months it will earn 51$ as interest.
hence answer is D

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mr.mohd: Newbie | Next Rank: 10 Posts; Posts: 2; Joined: Tue Jan 09, 2018 2:18 am

by mr.mohd » Sun Jan 28, 2018 11:29 pm

Do you think it should be E becasue the question says OVER $100 which means at least $100.1!!
Please correct me if I am mistaken

komal wrote:
bhumika.k.shah wrote:Donald plans to invest x dollars in a savings account that pays interest at an annual rate of 8% compounded quarterly. Approximately what amount is the minimum that Donald will need to invest to earn over $100 in interest within 6 months?

A .$1500
B. $1750
C. $2000
D. $2500
E. $3000

If its compounded quaterly = 3 months ...then shouldnt it be 16% for 6 months ?
Compound interest formula

A = P ( 1+r/n)power nt

given, n= 4 (quaterly);r =.08

the approach is substitution,

our interest requirement is 100$ after 6 months, 2 compounding period. interest per compounding period is 2%

lets take 1500, after 3 months interest accumulated is 30$, total amount is 1530
after 6 months, interest is 30.6$ and total is 1560.6$, so not 1500

1500 & 1750 have a difference of 250$ only , but the expected interest different is around 40$ hence you can straightaway rule out 1750

2000 is again can be ruled out as approx 4% interest yeilds only 80$

2500$ is a good bet, first 3 months it earns 50$ as interest, next 3 months it will earn 51$ as interest.
hence answer is D

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by [email protected] » Mon Jan 29, 2018 7:11 pm

Hi mr. mohd,

Since we're dealing with COMPOUND interest, we have to remember that with each 3-month period we're earning 'interest on top of interest.' This means that each 3-month period generates a bit more money than the 3-month period that immediately precedes it.

With $2500 and 2% interest per period, the first period would generate ($2500)(.02) = $50 of interest... and the 2nd period would generate a little MORE than that. Thus, we'll have OVER $100 in total interest at the end of the first 6 months.

Final Answer: D

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mr.mohd: Newbie | Next Rank: 10 Posts; Posts: 2; Joined: Tue Jan 09, 2018 2:18 am

TTT

by mr.mohd » Tue Jan 30, 2018 10:34 pm

Oh you're right!
Thank you

[email protected] wrote:Hi mr. mohd,

Since we're dealing with COMPOUND interest, we have to remember that with each 3-month period we're earning 'interest on top of interest.' This means that each 3-month period generates a bit more money than the 3-month period that immediately precedes it.

With $2500 and 2% interest per period, the first period would generate ($2500)(.02) = $50 of interest... and the 2nd period would generate a little MORE than that. Thus, we'll have OVER $100 in total interest at the end of the first 6 months.

Final Answer: D

GMAT assassins aren't born, they're made,
Rich

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by Scott@TargetTestPrep » Wed Jan 31, 2018 4:21 pm

bhumika.k.shah wrote:Donald plans to invest x dollars in a savings account that pays interest at an annual rate of 8% compounded quarterly. Approximately what amount is the minimum that Donald will need to invest to earn over $100 in interest within 6 months?

A .$1500
B. $1750
C. $2000
D. $2500
E. $3000

We can use the formula A = P(1 + r/n)^(nt) to solve this problem. Here P = x, r = 0.08, n = 4, and t = Â½ since 6 months = Â½ of a year, so nt = 4(Â½) = 2. Furthermore, let's assume the interest in 6 months is exactly $100; thus A = x + 100. Therefore, we can create the following equation:

x(1 + 0.08/4)^2 = x + 100

x(1.0404) - x = 100

.0404x = 100

x = 100/.0404 â‰ˆ 100/.04 = 2500

Answer: D

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