Final answer:
The future value of a $2000 deposit in an account earning 5% annual interest compounded quarterly after 10 years is approximately $3280.02, calculated using the compound interest formula.
Step-by-step explanation:
The question involves finding the future value of an investment that utilizes compound interest. The formula for the future value with compound interest 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 form), n is the number of times that interest is compounded per year, and t is the time the money is invested for in years.
Let's use this formula to find the account balance after 10 years for a $2000 deposit in an account that earns 5% annual interest compounded quarterly:
Principal, P= $2000
Annual interest rate, r = 5% or 0.05
Times compounded annually, n = 4 (quarterly)
Time, t = 10 years
Now, substitute these values into the formula:
A = 2000(1 + 0.05/4)^(4*10)
A = 2000(1 + 0.0125)^(40)
A = 2000(1.0125)^40
A ≈ 2000(1.640009)
A ≈ $3280.02
The account balance after 10 years will approximate $3280.02.