Respuesta :
Answer:
(a) $13811.68
(b) $13914.30
(c) $14004.55
(d) $14022.54
(e) $14023.15
Step-by-step explanation:
Since, the amount formula in compound interest,
[tex]A=P(1+\frac{r}{n})^{nt}[/tex]
Where,
P = Principal amount,
r = annual rate,
n = number of periods,
t = number of years,
Here, P = $ 9,400, r = 8% = 0.08, t = 5 years,
If the amount is compounded annually,
n = 1,
Hence, the amount of investment would be,
[tex]A=9400(1+\frac{0.08}{1})^5=9400(1.08)^5=\$ 13811.6839219\approx \$ 13811.68[/tex]
(a) If the amount is compounded annually,
n = 1,
The amount of investment would be,
[tex]A=9400(1+\frac{0.08}{1})^5=9400(1.08)^5=\$ 13811.6839219\approx \$ 13811.68[/tex]
(b) If the amount is compounded semiannually,
n = 2,
The amount of investment would be,
[tex]A=9400(1+\frac{0.08}{2})^{10}=9400(1.04)^{10}=\$13914.2962782\approx \$ 13914.30[/tex]
(c) If the amount is compounded Monthly,
n = 12,
The amount of investment would be,
[tex]A=9400(1+\frac{0.08}{12})^{60}=9400(1+\frac{1}{150})^{60}=\$ 14004.549658\approx \$ 14004.55[/tex]
(d) If the amount is compounded Daily,
n = 365,
The amount of investment would be,
[tex]A=9400(1+\frac{0.08}{365})^{365\times 5}=9400(1+\frac{2}{9125})^{1825}=\$ 14022.5375476\approx \$ 14022.54[/tex]
(e) Now, the amount in compound continuously,
[tex]A=Pe^{rt}[/tex]
Where, P = principal amount,
r = annual rate,
t = number of years,
So, the investment would be,
[tex]A=9400 e^{0.08\times 5}=9400 e^{0.4}=\$14023.1521578\approx \$14023.15[/tex]
