Final answer:
The final amount of money in an account after $2,700 is deposited at 3% interest compounded quarterly for ten years is $3,644.62, after applying the compound interest formula.
Step-by-step explanation:
To find the final amount of money in an account after $2,700 is deposited at a 3% interest compounded quarterly for ten years, we can use the formula for compound interest, which is A = P(1 + \frac{r}{n})^{nt}. Here, P is the principal amount ($2,700), r is the annual interest rate (0.03), n is the number of times interest is compounded per year (4, since it is compounded quarterly), and t is the time the money is invested for (10 years). Substituting these values into the formula, we get:
A = 2700(1 + \frac{0.03}{4})^{4*10}
A = 2700(1 + 0.0075)^{40}
A = 2700(1.0075)^{40}
A = 2700 * 1.349858807576003
A = $3644.62
Therefore, the final amount in the account after ten years would be $3,644.62, rounded to two decimal places.