Respuesta :
Answer:
n = 1, A = $4,096.54
n = 2, A = $4,109.04
n = 4, A = $4,115.39
n = 12, A = $4,119.66
n = 365, A = $4,121.73
Compounded continuously, A = $4,121.80
Step-by-step explanation:
We are given the following in the question:
P = $2500
r = 2.5% = 0.025
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 = 2500\bigg(1 + \displaystyle\frac{0.025}{1}\bigg)^{20}\\\\A = \$4,096.54[/tex]
For n = 2
[tex]A = 2500\bigg(1 + \displaystyle\frac{0.025}{2}\bigg)^{40}\\\\A = \$4,109.04[/tex]
For n = 4
[tex]A = 2500\bigg(1 + \displaystyle\frac{0.025}{4}\bigg)^{80}\\\\A = \$4,115.39[/tex]
For n = 12
[tex]A = 2500\bigg(1 + \displaystyle\frac{0.025}{12}\bigg)^{240}\\\\A = \$4,119.66[/tex]
For n = 365
[tex]A = 2500\bigg(1 + \displaystyle\frac{0.025}{365}\bigg)^{7300}\\\\A = \$4,121.73[/tex]
Continuous compounding:
[tex]A =Pe^{rt}\\A = 2500e^{0.025\times 20}\\A = \$4,121.80[/tex]
