Question

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?

Answer 1

$162.97 is the exact answer.

Explanation:

Answer 2

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:



`A=P(1+ (r)/(n) )^(nt)`


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:



`A=P(1+ (r)/(n) )^(nt)`


`A=4,000* (1+ (0.04)/(12) )^(12*1)=4,000(1+0.0033)^(12)`


`=4,000*1.0407=4162.97`


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 $.


Answer: $163