Answer
(a) $1033.82$ dollars.
(b) $963.42$ dollars.
(c) $11.90\ yr$.
Work Step by Step
(a) Given $P=1000, r=0.05, n=12, t=\frac{8}{12}=\frac{2}{3}\ yr$, we have $A=1000(1+\frac{0.05}{12})^{12\cdot \frac{2}{3}}\approx1033.82$ dollars.
(b) Given $A=1000, r=0.05, n=4, t=\frac{9}{12}=\frac{3}{4}\ yr$, we have $1000=P(1+\frac{0.05}{4})^{4\cdot \frac{3}{4}}$, thus $P=\frac{1000}{(1+\frac{0.05}{4})^{3}}\approx963.42$ dollars.
(c) Given $A=2P, r=0.06, n=1$, we have $2P=P(1+\frac{0.06}{1})^{t}$, thus $t=\frac{ln2}{ln(1+\frac{0.06}{1})}\approx11.90\ yr$.
