The compound interest formula for the amount of money A in an account after t years if a principal P is invested at an annual interest rate r (as a decimal) in n compounding periods a year is:
[tex]A=P(1+\frac{r}{n})^{nt}[/tex]In this case, the principal P is equal to 8074, the rate of 2.66% as a decimal is r=0.0266, the number of compounding periods a year is 365 and the time is equal to 6 years. Then, replace P=8074, r=0.0266, n=365 and t=6 to find the amount in the account after 6 years:
[tex]A=8074\times(1+\frac{0.0266}{365})^{365\times6}=9471.082482...[/tex]Subtract from the amount A the principal P to find how much interest will the account earn:
[tex]9471.082482...-8074=1397.082482...\approx1397.08[/tex]Therefore, to the nearest hundredth, the amount of interest that the account will earn is $1397.08.
