The answer is $1,059.34
Explanation:
The formula for compound interest is
I = P(1+[tex] \frac{r}{n} [/tex][tex] )^{nt} [/tex]
Where I = interest, P = principal (original deposit), r = interest rate, n = number of times compounded per year, and t = time, in years.
Using this formula, we can substitute the information from the question for the their corresponding variables.
Now, after filling in the information, your formula should look like this
I = 816(1+[tex] \frac{0.029}{365} [/tex][tex] )^{365*9} [/tex]
*The reason that the rate is 0.029 instead of 2.9 is that 2.9 is a percent, and we need a decimal. To convert it, you just need to divide the percent by 100.
Now, all we need to do is solve the equation using order of operations (PEMDAS).
I will divide the 0.029 by 365 first.
I = 816(1+0.00008[tex] )^{365*9} [/tex]
**This is not the exact decimal. It would be too difficult to write entirely, but I will be using the true decimal in my calculations.
Next, we have to add 1 to the decimal.
I = 816(1.00008[tex] )^{365*9} [/tex]
Now, I will multiply 365 and 9 together.
I = 816(1.00008[tex] )^{3285} [/tex]
Next, we must raise the number within the parenthesis to the power of 3285.
I = 816(1.3)
***Again, this is not the actual decimal. The real one will be used in the calculation, though, like before.
Finally, we have to multiply the decimal by the principal, 816.
I = $1,059.34
