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Sagot :
The formula to be using is as follows:
[tex]A=P(1+\frac{r}{n})^{nt}[/tex]But A is the total amount, that is, the initial amount plus the interest amount. If we want just theinterest, I, we need to substract the initial amount:
[tex]\begin{gathered} I=A-P \\ I=P(1+\frac{r}{n})^{nt}-P \end{gathered}[/tex]The given information are:
[tex]\begin{gathered} P=12000 \\ r=0.08 \\ n=1 \\ t=4 \end{gathered}[/tex]Where r was converted from percentage to decimal and n is 1 because it is compounded only once per year.
So, substituting these values, we have:
[tex]\begin{gathered} I=P(1+\frac{r}{n})^{nt}-P \\ I=12000(1+\frac{0.08}{1})^{1\cdot4}-12000 \\ I=12000(1+0.08)^4-12000 \\ I=12000(1.08)^4-12000 \\ I=12000\cdot1.36048\ldots-12000 \\ I=16325.867\ldots-12000 \\ I=4325.867\ldots\approx4325.87 \end{gathered}[/tex]So, the interest amount is approximately $4,325.87.
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