Answer:
18.85 years
Step-by-step explanation:
Using the [tex]A=P(1+\frac{r}{n} )^{nt}[/tex] we can manipulate it to give us time.
However, let's identify our variables:
A is our final amount which is given to us, $1400.
P is our principle which is $500.
r is our rate which is 5.5% which can be traducted into 0.055.
n is the # of time our money get compounded per year, in this case quarterly means 4 times a year therefore n = 4.
t is time and is what we are trying to solve for.
Now let's manipulate our equation to find t:
[tex]A=P(1+\frac{r}{n} )^{nt}[/tex]
[tex]\frac{A}{P} =(1+\frac{r}{n} )^{nt}[/tex]
[tex]\frac{1400}{500} =(1+\frac{0.055}{4} )^{4t}[/tex]
[tex]2.8=1.01375^{4t}[/tex]
[tex]log_{1.01375}(2.8)=log_{1.01375}1.01375^{4t}[/tex]
[tex]log_{1.01375}(2.8)=4t[/tex]
[tex]\frac{log_{1.01375}(2.8)}{4} =t[/tex]
[tex]18.84876253=t[/tex]
It would take about 18.85 years in order for you to accumulate at least $1400.
