Final answer:
Emilio and Audrey will have $1,040.40 after 2 years to spend on their trip, which is calculated using the compound interest formula with a principal of $1,000, a 2% interest rate, and compounded annually.
Step-by-step explanation:
Emilio and Audrey want to know how much they will have after 2 years if they deposit $1,000.00 in a savings account with a 2% interest rate compounded annually. To find the total amount they can spend on their trip, we use the formula for compound interest, which is A = P(1 + r/n)^(nt), 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 (in decimal), n is the number of times that interest is compounded per year, and t is the time the money is invested for in years.
In this case, P = $1,000, r = 0.02 (2% as a decimal), n = 1 (since the interest is compounded annually), and t = 2 years. Plugging these values into the formula, we get:
A = $1,000(1 + 0.02/1)^(1×2) = $1,000(1.02)^2 = $1,000×1.0404 = $1,040.40
Therefore, Emilio and Audrey will be able to spend $1,040.40 on their trip in 2 years.