Answer
(a) $\$4221.81$
(b) $\$5092.47$
(c) $\$6142.69$
Work Step by Step
The formula to calculate the value of an investment that is compounded continuously at a given rate is $P(t)=Pe^{(r)(t)}$
Where $P(t)=$ the value of an investment at $t$, $P=$principal amount, $r= rate$, and $t= time$
From the question we know that $P=3500$ and $r= .0625$ giving us the formula
$P(t)=3500e^{(.0625)(t)}$
What is the value of the investment after
(a) $3$ years
$P(3)=3500e^{(.0625)(3)}$
$p(3)= 4221.81 \$$
(b) $6$ years
$P(6)=3500e^{(.0625)(6)}$
$p(6)= 5092.47 \$$
(c) $9$ years
$P(9)=3500e^{(.0625)(9)}$
$P(9)= 6142.69 \$$
