When an amount [tex]P[/tex] is invested for [tex]t[/tex] years during which it earns an interest of [tex]r[/tex] dollars compounded [tex]m[/tex] times per year, the formula to calculate the amount that investment grows to after [tex]t[/tex] years is,
[tex]A=P(1+\tfrac{r}{m})^{mt}.[/tex]
Assuming that a years has 365 days ,the values for each of these variables is given as follows, [tex]m=365[/tex] ,[tex]t=6[/tex][tex]r=8.5\%=0.085 .[/tex] The value of the investment after 6 years is then calculated as shown below,
[tex]A=P(1+\tfrac{r}{m})^{mt}\\A=6000(1+\tfrac{0.085}{365})^{(365\times 6)}\\A=9991.15[/tex]
The investment grows to reach $9991.15 in 6 years.
