Answer
$A(1)\approx\$7213.18$
$A(2)\approx\$7432.86$
$A(3)\approx\$7659.22$
$A(4)\approx\$7892.48$
$A(5)\approx\$8132.84$
$A(6)\approx\$8380.52$
Work Step by Step
*For a quick review*
For Continuously Compounded Interest we have the following formula (Also explained in this chapter, 4.2):
$A(t)=Pe^{rt}$
$t$ - number of years
$r$ - interest rate per year
$P$ - principal
$A(t)$ - amount of money after $t$ years
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We have an investment of $\$7000$ and $r=3\%=0.03$, so the formula will get the following form:
$A(t)=7000e^{0.03t}$
$A(1)=7000e^{0.03\times1}=7000e^{0.03}\approx\$7213.18$
$A(2)=7000e^{0.03\times2}=7000e^{0.06}\approx\$7432.86$
$A(3)=7000e^{0.03\times3}=7000e^{0.09}\approx\$7659.22$
$A(4)=7000e^{0.03\times4}=7000e^{0.12}\approx\$7892.48$
$A(5)=7000e^{0.03\times5}=7000e^{0.15}\approx\$8132.84$
$A(6)=7000e^{0.03\times6}=7000e^{0.18}\approx\$8380.52$