Janise smithson invested $4,000 for one year in a cd that earns interest at a rate of 4% compounded monthly. what is the interest earned during the year?

Let:
 
P be the initial amount of money called the Principal, 

compounded n times a year, with an r annual interest rate, then after

t many years, the amount of money A is given by the formula:



Remark
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r is generally a percentage like 3%, 7% etc and are applied in the formula as 0.03, 0.07..., 

the interest is compounded generally annually (n=1), quarterly (n=4), monthly (n=12), etc...

t is in years,

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Thus, in our problem, P=$4,000, r=4%=0.04, n=12, t=1

Applying the formula:







At the end of the year Janise has 4,162.97-4,000≈163 more dollars than the Principal amount.

Thus, the interest earned during the year is 163 $.

 $163