Answer
(a) When $rate=2\%$
$A\approx\$10169.99$
(b) When $rate=3\%$
$A\approx\$11466.63$
(c) When $rate=4.5\%$
$A\approx\$13728.05$
(d) When $rate=7\%$
$A\approx\$18530.93$
Work Step by Step
*A quick review*
For Continuously Compound Interest we have the following formula (Also explained in previous chapters):
$A = Pe^{rt}$
$t$ - number of years
$r$ - interest rate per year (In decimal form)
$P$ - principal
$A$ - amount of money after $t$ years
---
In this case we know $P=8000$, $t=12$; so we will use: $A(r)=8000e^{12r}$
(a) When $r=2\%=0.02$
$A(r)=8000e^{12\times0.02}=8000e^{0.24}\approx\$10169.99$
(b) When $r=3\%=0.03$
$A(r)=8000e^{12\times0.03}=8000e^{0.36}\approx\$11466.63$
(c) When $r=4.5\%=0.045$
$A(r)=8000e^{12\times0.045}=8000e^{0.54}\approx\$13728.05$
(d) When $r=7\%=0.07$
$A(r)=8000e^{12\times0.07}=8000e^{0.84}\approx\$18530.93$