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GRE Prep Club Team Member
Joined: 20 Feb 2017
Posts: 2506
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How much more interest will maria receive if she invests 1000$ for one
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09 Apr 2022, 02:51
09 Apr 2022, 02:51
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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. x220
D. x240
E. (10x+x240)
A. 5x
B. 10x
C. x220
D. x240
E. (10x+x240)
Re: How much more interest will maria receive if she invests 1000$ for one
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10 Apr 2022, 18:08
10 Apr 2022, 18:08
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two cases
Interest (1): 1.000 (1+x)
Interest (2): 1.000 (1+x/2)²
1.000 [1²+2.1.(x/2)+(x/2)²
1.000 [1+2.1.(x/2)+(x/2)²]
1.000 [1+x+x²/4]
Comparing (1) and (2), you can notice that extra interest is x²/4
Interest (1): 1.000 (1+x)
Interest (2): 1.000 (1+x/2)²
1.000 [1²+2.1.(x/2)+(x/2)²
1.000 [1+2.1.(x/2)+(x/2)²]
1.000 [1+x+x²/4]
Comparing (1) and (2), you can notice that extra interest is x²/4
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Re: How much more interest will maria receive if she invests 1000$ for one
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06 May 2022, 01:14
06 May 2022, 01:14
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GeminiHeat 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. x220
D. x240
E. (10x+x240)
A. 5x
B. 10x
C. x220
D. x240
E. (10x+x240)
Its quicker if we assume some value of x
Let x = 10
C.I (Compounded semi-annually) = 1000(1+10200)2=1000(1.05)2=$1102.5
C.I (Compounded annually) = 1000(1+10100)1=1000(1.1)1=$1100
How much more?
$2.5 more
Now, put the value of x as 10 and see which option is giving us 2.5?
A. 5x
5(10) = 50
B. 10x
10(10) = 100
C. x220
10220=5
D. x240
10240=2.5
E. (10x+x240)
(10(10)+10240)=102.5
Hence, option D
