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

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.

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.

GMAT assassins aren't born, they're made,
Rich

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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