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Elliot and Faye invest \$5000 each in different banks

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Intern
Joined: 30 Aug 2017
Posts: 15
Elliot and Faye invest \$5000 each in different banks [#permalink]

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17 Sep 2017, 20:47
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Difficulty:

35% (medium)

Question Stats:

67% (01:09) correct 33% (01:25) wrong based on 45 sessions

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Elliot and Faye invest \$5000 each in different banks. Elliot earns annual rate of interest 12% compounded monthly and Faye earns annual rate of interest 12% compounded quarterly. If after 6 months Elliot earns a total interest of E, and Faye earns a total interest of F, which of the following must be true?

A. E=F
B. E>F
C. E<F
D. E=\$300
E. F=\$300
Manager
Joined: 22 May 2015
Posts: 106
Elliot and Faye invest \$5000 each in different banks [#permalink]

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17 Sep 2017, 22:39
Elliot and Faye invest \$5000 each in different banks. Elliot earns annual rate of interest 12% compounded monthly and Faye earns annual rate of interest 12% compounded quarterly. If after 6 months Elliot earns a total interest of E, and Faye earns a total interest of F, which of the following must be true?

A. E=F
B. E>F
C. E<F
D. E=\$300
E. F=\$300

Need to input numbers and solve.

Amount Elliot earns after 6 months is \$5307.60 while Faye earns \$5304.50. Interest earned by Elliot is greater than interest earned by Faye.
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SC Moderator
Joined: 22 May 2016
Posts: 1753
Elliot and Faye invest \$5000 each in different banks [#permalink]

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18 Sep 2017, 09:32
1
Elliot and Faye invest \$5000 each in different banks. Elliot earns annual rate of interest 12% compounded monthly and Faye earns annual rate of interest 12% compounded quarterly. If after 6 months Elliot earns a total interest of E, and Faye earns a total interest of F, which of the following must be true?

A. E=F
B. E>F
C. E<F
D. E=\$300
E. F=\$300

No need to calculate, if compound interest is familiar. (If not, see the rule below.) Principal amounts, interest rates, and time are identical. E gets paid more times than F. E will be greater than F.

The rule is: All else being equal (principal, interest rate, and time period), whoever gets paid "interest on interest" more frequently has the highest rate of return and highest future value over time.

If more frequent installments = greater future value, then Elliott wins. Elliott gets paid compounding interest 12 times a year, or 6 times in 6 months. Faye gets paid compounding interest 4 times a year, or 2 times in six months.

No matter what, over time, Elliott earns more "interest on interest."

But if you sense that the difference is not huge (and it is not here - six months is too short a time), and you want to be sure . . . you can choose an easier principal amount and round a little.

\$10,000 at 12%? Choose a big principal. For rate, stay with 12 percent for ease of division.

E gets .12/12 = .01 every month
F gets .12/4 = .03 every 3 months

Amount with interest added in, for months 1-6:

E: 10100, 10201, 10303, 10406, 10510, 10615

F: 10000, 10000, 10300, 10300, 10300, 10,609

E > F

Actual difference here is not huge. After six months:
Elliott has \$5,307.60
And Faye has \$5,304.50

Still, E has about \$3.00 more. That is all that matters. Over time, E will be greater than F by quite a bit.
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In the depths of winter, I finally learned
that within me there lay an invincible summer.

GMAT Forum Moderator
Joined: 28 May 2014
Posts: 528
GMAT 1: 730 Q49 V41
Re: Elliot and Faye invest \$5000 each in different banks [#permalink]

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05 Oct 2017, 08:31
You can answer this without calculation.

If investment amount and interest rate is same, the amount which is compounded more frequently will be greater.

for same amount and interest rate, the total interest earned for 6 months will be:

compounded daily > compounded weekly > compounded monthly > compounded half-yearly

Ans: B.
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Manager
Joined: 28 Sep 2017
Posts: 82
Location: India
Concentration: General Management
GMAT 1: 740 Q49 V42
GPA: 3.92
Re: Elliot and Faye invest \$5000 each in different banks [#permalink]

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05 Oct 2017, 10:05
Interest rate for 6 months of E would be greater than interest rates for 6 months of F.
Rest all variables same.
So E > F
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Re: Elliot and Faye invest \$5000 each in different banks   [#permalink] 05 Oct 2017, 10:05
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