Answer
(a) $1033.82$ dollars.
(b) $963.42$ dollars.
(c) $11.9$ years.
Work Step by Step
(a) Given $P=1000, r=0.05, n=12, t=\frac{8}{12}=\frac{2}{3}$, we have $A=P(1+\frac{r}{n})^{nt}=1000(1+\frac{0.05}{12})^{12(2/3)}\approx1033.82$ dollars.
(b) Given $A=1000, r=0.05, n=4, t=\frac{9}{12}=\frac{3}{4}$, we have $A=P(1+\frac{r}{n})^{nt}\Longrightarrow 1000=P(1+\frac{0.05}{4})^{4(3/4)} \Longrightarrow P\approx963.42$ dollars.
(c) Given $A=2P, r=0.06, n=1$, we have $A=P(1+\frac{r}{n})^{nt}\Longrightarrow 2P=P(1+\frac{0.06}{1})^{t} \Longrightarrow t=\frac{ln2}{ln1.06}\approx11.9$ years.
