Answer:
The value of the acount after t years is of [tex]A(t) = 650(1.0072)^{12t}[/tex]
The annual growth rate is of 0.72%.
Step-by-step explanation:
Compound interest:
The compound interest formula is given by:
[tex]A(t) = P(1 + \frac{r}{n})^{nt}[/tex]
Where A(t) is the amount of money after t years, P is the principal(the initial sum of money), r is the interest rate(as a decimal value), n is the number of times that interest is compounded per year and t is the time in years for which the money is invested or borrowed.
$650 is invested in an account earning 8.6% interest (APR), compounded monthly.
This means that [tex]P = 650, r = 0.086, n = 12[/tex]. So
[tex]A(t) = P(1 + \frac{r}{n})^{nt}[/tex]
[tex]A(t) = 650(1 + \frac{0.086}{12})^{12t}[/tex]
[tex]A(t) = 650(1.0072)^{12t}[/tex]
The value of the acount after t years is of [tex]A(t) = 650(1.0072)^{12t}[/tex]
Annual growth rate
1.0072 - 1 = 0.0072 = 0.72%
The annual growth rate is of 0.72%.
