A new savings account offers 6 percent annual interest compounded every 6 months. What would be the total balance in an account after 1 year, if the initial amount in the account were $6000?

A. $80.00
B. $84.40
C. $360.00
D. $6,360.00
E. $6,365.40


(E) The interest is compounded every 6 months. To calculate interest, you must take the principal and multiply it by the interest and the length of time (using the unit used in the interest, typically years). At the end of the first 6 months the interest earned is $6,000(.06) (1/2) = $180. (Note: the 6 months are “1/2” in the equation since 6% is a yearly rate, not a bi-yearly one).

Since the interest is compounded, the second six months of the year are not earning interest on just the original $6,000, but on the interest as well, so they are actually earning interest on $6,180. The interest earned during the final 6 months of the year is $6,180(.06)(1/2) = $185.4. Therefore, the total balance is the original amount ($6000) + $180 + $185.40 = $6,365.40. The correct answer is E.
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How come does the compound interest formula not render the same result?

It does. Note that the interest is compounded every 6 months, while the given interest rate is the annual one. So the formula to use is:

F = I × (1 + r/n)ⁿª, where

F – final amount
I – initial amount
r – annual interest rate
n – number of times the interest is compounded per year
a – number of years

The interest is compounded every 6 months, in other words twice a year. Plug it in the formula along with other values:

F = $6,000(1 + 0.06 / 2) ²
F = $6365.4