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How much more interest will maria receive if she invests 1000$ for one

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Re: How much more interest will maria receive if she invests 1000$ for one  [#permalink]

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New post 27 Jan 2018, 13:48
Hi All,

This question requires knowledge of the formulas for Simple Interest and Compound Interest:

Simple Interest = Principal x (1 + RT)
Compound Interest = Principal x (1 + R)^T

Where R is the yearly interest rate and T is the number of years. When compounding MORE than once a year, you must divide R by the number of periods and multiply T by the same number of periods.

We're asked for the DIFFERENCE in the amount of interest that is generated under two different situations. We can TEST VALUES to answer this question. IF... X = 20...

$1,000 at 20% compounded semi-annually (meaning twice a year) =

$1,000 x (1.1)^2 =
$1,000 x (1.21) = $1210

$1,000 at 10% compounded annually =

$1,000 x (1.2)^1 =
$1200

The difference is $10, so we're looking for an answer that equals 10 when we plug X=20 into it. There's only one answer that matches....

Final Answer:
Spoiler: ::
D


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Re: How much more interest will maria receive if she invests 1000$ for one  [#permalink]

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New post 28 Jan 2018, 20:50
[quote="FightToSurvive"]How much more interest will maria receive if she invests 1000$ for one year at x % annual interest, compounded semianually, than if she invest 1000$ for one year at x percent annual interest, compounded annually?

a> 5x
b> 10x
c> x^2/20
d> x^2/40
e>10x+ (x^2/40)

I dont from what source these questions are from.
See from simplification sake, take x =10%
(i) investing 1000$ for one year at x % annual interest, compounded semiannually
1000*1.05*1.05=1102.5
Interest amount = 1102.5-1000=102.5
(ii)investing 1000$ for one year at x percent annual interest, compounded annually
1000*1.1=1100
Interest amount = 1100-1000=100
Difference in two cases = 102.5-100 = 2.5

Putting x=10 in the above option , D gives you the answer
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How much more interest will maria receive if she invests 1000$ for one  [#permalink]

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New post 20 Aug 2018, 07:09
can we use the concept that CI will be slightly larger than SI. hence the difference should also be slightly larger.


in this case, the difference in SI is 0 hence the difference in CI should be slightly larger than 0. Hence x^2/40 is the smallest number out of all and should be the answer.

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Re: How much more interest will maria receive if she invests 1000$ for one  [#permalink]

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New post 26 Nov 2018, 06:09
Just take x = 200%
You can solve it in a minute!
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Re: How much more interest will maria receive if she invests 1000$ for one  [#permalink]

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New post 03 Jan 2019, 09:28
email2vm wrote:
How much more interest will maria receive if she invests 1000$ for one year at x % annual interest, compounded semianually, than if she invest 1000$ for one year at x percent annual interest, compounded annually?


A. 5x

B. 10x

C. \(\frac{x^2}{20}\)

D. \(\frac{x^2}{40}\)

E. \((10x+\frac{x^2}{40})\)


Spoiler: ::
Here is how i solved only to get it wrong:

let x=100%

annually :

SI = 1000*100/100*1 = 1000
total =1000+1000=2000

semiannually:

Si (for 1st 6 months) = 1000
total after 6 months =2000

Si(for last 6 months) = 2000
total after 6 months= 4000

more interest maria will receive = 2000

====looking for the answer choices

100^2/40 != 2000!!!

where am I wrong? Today it seems I am back to square 1



It is easier to test numbers in this question. Try with x = 20%. One can solve this question in less than 2 minutes.
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Re: How much more interest will maria receive if she invests 1000$ for one  [#permalink]

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New post 10 Jul 2019, 14:48
Got this wrong on an official practice test. Resolving here for retention:

Method 1 - Plug-in values for x (quickest method)

x= 20

Compounded
New balance after compounding is equal to 1000(1+20/200)^2
= 1000(11/10)^2
= 1000(121/100)
= 1210

Simple interest
New balance with interest 1000(1+20/100)^1
= 1000(6/5)
= 1200

'How much more interest' = 1210 - 1200 = 10 more

Plug-in 20 to each answer choice to get 10
A - 5(20) = 200 --> Wrong
B - 10(20) = 200 --> wrong
C - (20)^2/ 20 = 20 --> wrong
D - (20)^2/40 = 10 --> correct
E - (10(2) + (20)^2/40) = 30 --> wrong


Method 2 - Algebraic, but since we have variables, breakdown the compounding periods instead of calculating it all in one go)


Compounding:
1000(1+x/100/2)^1
= 1000 (1 + x/200)^1
= 1000 + 5x
New balance after first compounding period = 1000 + 5x

Second compounding period
Principle *(Interest rate/#compound periods + 1)^compounding period
(1000 + 5x)(1 + x/200)^1
= 1000 + 5x + 5x + (5x^2)/200
= 1000 + 10x + x^2/40
Now we need to eliminate the principle to get the interest portion
= 1000 + 10x + x^2/40 - 1000
= 10x + x^2/40

Simple interest amount
1000(1+ x/100)^1
= 1000 + 10x
Interest portion = 1000+10x - 1000
= 10x

How much more interest?
= 10x + x^2/40 - 10x
= x^2/40
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Re: How much more interest will maria receive if she invests 1000$ for one   [#permalink] 10 Jul 2019, 14:48
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