Answer
(a) (i) $A(3) = \$1259.71$
(ii) $A(3) = \$1268.24$
(iii) $A(3) = \$1270.23$
(iv) $A(3) = \$1271.01$
(v) $A(3) = \$1271.22$
(vi) $A(3) = \$1271.25$
(vii) $A(3) = \$1271.25$
(b) We can see a sketch of the three graphs below.
Work Step by Step
(a) $A(t) = A(0)~(1+\frac{r}{n})^{nt}$
(i) $A(3) = (1000)(1+\frac{0.08}{1})^{3} = \$1259.71$
(ii) $A(3) = (1000)(1+\frac{0.08}{4})^{12} = \$1268.24$
(iii) $A(3) = (1000)(1+\frac{0.08}{12})^{36} = \$1270.23$
(iv) $A(3) = (1000)(1+\frac{0.08}{52})^{156} = \$1271.01$
(v) $A(3) = (1000)(1+\frac{0.08}{365})^{1095} = \$1271.22$
(vi) $A(3) = (1000)(1+\frac{0.08}{365\cdot 24})^{1095} = \$1271.25$
(vii) $A(3) = (1000)e^{(0.08)(3)} = \$1271.25$
(b) We can see a sketch of the three graphs below.
$A(t) = (1000)e^{0.06~t}$
$A(t) = (1000)e^{0.08~t}$
$A(t) = (1000)e^{0.10~t}$
