It looks like you need help with a compound interest problem. The formula for compound interest is:
[tex]\[ A = P \left(1 + \frac{r}{n}\right)^{nt} \][/tex]
where:
- \( A \) is the amount of money accumulated after n years, including interest.
- \( P \) is the principal amount (the initial amount of money).
- \( r \) is the annual interest rate (decimal).
- \( n \) is the number of times that interest is compounded per year.
- \( t \) is the time the money is invested for, in years.
Given the information from your image:
- [tex]\( P = $2,700 \)[/tex]
- [tex]\( r = 2\% = 0.02 \)[/tex]
- [tex]\( n = 4 \)[/tex] (because interest is compounded quarterly)
- [tex]\( t = 8 \)[/tex] years
We can now plug these values into the formula to find the final amount. Let's calculate that.
The final amount of money in the account after 8 years, with $2,700 deposited at 2% interest compounded quarterly, would be $3,167.22 when rounded to two decimal places.
