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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....

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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
Re: How much more interest will maria receive if she invests 1000$ for one   [#permalink] 28 Jan 2018, 20:50

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