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Ms. Lopez deposits $ 100 in an account that pays 20% interest, compoun

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Ms. Lopez deposits $ 100 in an account that pays 20% interest, compoun [#permalink]

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New post 03 Jan 2016, 12:10
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Ms. Lopez deposits $ 100 in an account that pays 20% interest, compounded semiannually. How much money will there be in the account at the end of one year?

A. $118.00
B. $120.00
C. $121.00
D. $122.00
E. $140.00

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Re: Ms. Lopez deposits $ 100 in an account that pays 20% interest, compoun [#permalink]

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New post 04 Jan 2016, 22:26
Bunuel wrote:
Ms. Lopez deposits $ 100 in an account that pays 20% interest, compounded semiannually. How much money will there be in the account at the end of one year?

A. $118.00
B. $120.00
C. $121.00
D. $122.00
E. $140.00


Hi,
let me explain the concept for those who are not familiar with compounded semi annually/ quarterly etc..
it basically means, here, that the interest will be paid twice, after 6 months and at the end of year..so twice..
but interest is 20%, which will get distributed semiannually that is 10%...
so the Q literally means ..
after 6 months..
100*10/100 + 100=110..
at the end of year
110*10/100 + 110= 121..

or we put it in compound interest formula..
where CI=10%, T is 2 and P=100..
so amount = 100(1 + 10/100)^2=100*1.1*1.1=121..
C
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Re: Ms. Lopez deposits $ 100 in an account that pays 20% interest, compoun [#permalink]

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New post 05 Jan 2016, 14:31
Ans C

Using Formula - A = P(1+r/n)^nt

Given
P=100
n=2
t=1
r=0.2

Substituting value in formula

A = 100(1+0.2/2)^2

A= 121.00$

Thank You



Bunuel wrote:
Ms. Lopez deposits $ 100 in an account that pays 20% interest, compounded semiannually. How much money will there be in the account at the end of one year?

A. $118.00
B. $120.00
C. $121.00
D. $122.00
E. $140.00
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Re: Ms. Lopez deposits $ 100 in an account that pays 20% interest, compoun [#permalink]

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New post 05 Jan 2016, 19:28
initial deposit 100 rs 20% compounded semiannually.

semianually means compounded for 6 months.

here 20% becomes 10% and compounded twice per year,

then 100 rs becomes 110 after six months, and becomes 121 after one year.
so option C is correct.
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Re: Ms. Lopez deposits $ 100 in an account that pays 20% interest, compoun [#permalink]

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New post 07 Jan 2016, 14:21
Hi All,

The formula for Compound Interest is...

(Principal)(1 + R)^T where R is the interest rate (as a decimal) and T is the length of time (almost always in years).

Although it's relatively rare, the GMAT might ask you to deal with interest that is calculated MORE OFTEN than once a year. When that occurs, you have to make some adjustments to the above formula.

For example, if interest in calculated TWICE a year, then T is DOUBLED, but R is HALVED.

In that same way, if interest is calculated THREE TIMES a year, then T is TRIPLED, but R is DIVIDED BY 3.

Etc.

In this question, calculating interest SEMI-ANNUALLY means "twice a year", so the variables become T=2 and R=10; you can then calculate the answer.

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Ms. Lopez deposits $ 100 in an account that pays 20% interest, compoun [#permalink]

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New post 18 May 2017, 13:19
Ms. Lopez deposits $ 100 in an account that pays 20% interest, compounded semiannually. How much money will there be in the account at the end of one year?
A. $118.00
B. $120.00
C. $121.00
D. $122.00
E. $140.00

Amount = P \((1 + \frac{R}{100})^n\) (P = Principal, R = Rate of interest, n = Time)
Rate of interest is compounded semi- annually = \(\frac{20}{2}\) = 10% in 6 months
Therefore n = 2 (Annually is 12 months, Compounded semi - annually is 6 months = \(\frac{12}{6}\) = 2)
Amount = 100 \((1 + \frac{10}{100})^2\) = 100 * \(\frac{11}{10} *\frac{11}{10}\) = $121
Answer C...

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Ms. Lopez deposits $ 100 in an account that pays 20% interest, compoun   [#permalink] 18 May 2017, 13:19
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Ms. Lopez deposits $ 100 in an account that pays 20% interest, compoun

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