Respuesta :
Answer:
[tex] n=1, A=17599.97[/tex]
[tex] n=2, A=18023.91[/tex]
[tex] n=4, A=18245.052[/tex]
[tex] n=12, A=18395.45[/tex]
[tex] n=365, A=18470.02[/tex]
Step-by-step explanation:
P=$2500
r = 5%
t = 40 years
A= ? for n= 1, 2, 4, 12, 365
Continuous compounding is given by
[tex]A=P(1+\frac{r}{n} )^{nt}[/tex]
[tex]A=2500(1+\frac{0.05}{n} )^{n*40}[/tex]
For n=1
[tex]A=2500(1+\frac{0.05}{1} )^{1*40}=2500(7.039988) =17599.97[/tex]
For n=2
[tex]A=2500(1+\frac{0.05}{2} )^{2*40}=2500(7.209567) =18023.91[/tex]
For n=4
[tex]A=2500(1+\frac{0.05}{4} )^{4*40}=2500(7.2980208) =18245.052[/tex]
For n=12
[tex]A=2500(1+\frac{0.05}{12} )^{12*40}=2500(7.3581828) =18395.45[/tex]
For n=365
[tex]A=2500(1+\frac{0.05}{365} )^{365*40}=2500(7.3880115) =18470.02[/tex]
As the value of n keeps on increasing the value of A is coming to a steady value thus we approximate this by using exponential function
[tex]A=Pe^{rt}[/tex]
[tex]A=2500e^{0.05*40}=18472.64[/tex]
As you can see it is almost equal to our answer calculated earlier for n=365
