Respuesta :
Answer:
n = 1, A = $2,191.12
n = 2, A = $2,208.04
n = 4, A = $2216.71
n = 12, A = $2222.58
n = 365, A = $2225.44
Compound continuously, A = $2,225.54
Step-by-step explanation:
We are given the following in the question:
P = $1000
r = 4% = 0.04
t = 20 years
Formula:
The compound interest is given by
[tex]A = P\bigg(1 + \displaystyle\frac{r}{n}\bigg)^{nt}[/tex]
where P is the principal, r is the interest rate, t is the time, n is the nature of compound interest and A is the final amount.
For n = 1
[tex]A = 1000\bigg(1 + \displaystyle\frac{0.04}{1}\bigg)^{20}\\\\A = \$2,191.12[/tex]
For n = 2
[tex]A = 1000\bigg(1 + \displaystyle\frac{0.04}{2}\bigg)^{40}\\\\A = \$2,208.04[/tex]
For n = 4
[tex]A = 1000\bigg(1 + \displaystyle\frac{0.04}{4}\bigg)^{80}\\\\A = \$2216.71[/tex]
For n = 12
[tex]A = 1000\bigg(1 + \displaystyle\frac{0.04}{12}\bigg)^{240}\\\\A = \$2222.58[/tex]
For n = 365
[tex]A = 1000\bigg(1 + \displaystyle\frac{0.04}{365}\bigg)^{7300}\\\\A = \$2225.44[/tex]
Compounded continuously:
[tex]A = Pe^{rt}\\A = 1000e^{0.04\times 20}\\A = $2,225.54[/tex]
