Respuesta :
Solution:
The amount earned after a given period of time on an amount invested at a given interest rate is expressed as
[tex]\begin{gathered} A=P(1+rt)\text{ ---- equation 1} \\ where \\ A\Rightarrow amount\text{ earned} \\ P\Rightarrow amount\text{ invested} \\ r\Rightarrow interest\text{ rate} \\ t\Rightarrow time \end{gathered}[/tex]Given that you obtain a $6300 bond that pays 2% interest annually that matures in 5 years, this implies that
[tex]\begin{gathered} P=6300 \\ r=2\%=0.02 \\ t=5 \end{gathered}[/tex]By substituting these values into the above formula, we have
[tex]\begin{gathered} A=6300(1+(0.02\times5)) \\ =6300(1.1) \\ =6930 \end{gathered}[/tex]This implies that the amount earned after 5 years is $6390.
To evaluate the interest earned, we subtract the amount invested from the amount earned.
Thus,
[tex]\begin{gathered} I=A-P \\ where \\ I\Rightarrow interest\text{ earned} \\ thus, \\ I=6930-6300 \\ \Rightarrow I=\$630 \end{gathered}[/tex]Hence, the interest earned is evaluated to be
[tex]\$630[/tex]