Answer:
338 (1 Year)
365.58 (3 Years)
427.68 (7 Years)
712.12 (20 Years)
Step-by-step explanation:
To find the compounded annual value, we use the formula:
[tex]A = P(1 + r/n)^{nt}[/tex]
Let's first take each variable and list them:
P = 325
r = 4% or 0.04
t = 1, 3, 7, 20
n = 1
Let's take each number of years one at a time.
[tex]A = P(1 + r/n)^{nt}[/tex]
After 1 Year
[tex]A = 325(1 + \dfrac{0.04}{1})^{1(1)}[/tex]
[tex]A = 325(1 + \frac{0.04}{1})^{1}[/tex]
[tex]A = 325(1 + 0.04)^{1}[/tex]
[tex]A = 325(1.04)^{1}[/tex]
[tex]A = 325(1.04)[/tex]
[tex]A = 338[/tex]
After 3 Years
[tex]A = 325(1 + \dfrac{0.04}{1})^{1(3)}[/tex]
[tex]A = 325(1 + \frac{0.04}{1})^{3}[/tex]
[tex]A = 325(1 + 0.04)^{3}[/tex]
[tex]A = 325(1.04)^{3}[/tex]
[tex]A = 325(1.1248)[/tex]
[tex]A = 365.58[/tex]
After 7 Years
[tex]A = 325(1 + \dfrac{0.04}{1})^{1(7)}[/tex]
[tex]A = 325(1 + \frac{0.04}{1})^{7}[/tex]
[tex]A = 325(1 + 0.04)^{7}[/tex]
[tex]A = 325(1.04)^{7}[/tex]
[tex]A = 325(1.3159)[/tex]
[tex]A = 427.68[/tex]
After 20 years
[tex]A = 325(1 + \dfrac{0.04}{1})^{1(20)}[/tex]
[tex]A = 325(1 + \frac{0.04}{1})^{20}[/tex]
[tex]A = 325(1 + 0.04)^{20}[/tex]
[tex]A = 325(1.04)^{20}[/tex]
[tex]A = 325(2.1911)[/tex]
[tex]A = 712.12[/tex]
