Final answer:
The correct expression for the amount in a CD after t years with a 2.1% annual interest rate compounded monthly is P(1.00175)^(12t), using the compound interest formula A = P(1 + r/n)^(nt).
Step-by-step explanation:
If Stephen is considering investing money in a certificate of deposit (CD) that offers an annual interest rate of 2.1% compounded monthly, the correct expression to represent the amount of money in the account after t years can be found using the compound interest formula: 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 (decimal), n is the number of times that interest is compounded per year, and t is the time in years.
For the given CD, with a 2.1% annual rate compounded monthly, we have:
- Annual interest rate (r): 0.021 (as a decimal)
- Times compounded annually (n): 12 (since monthly)
The correct expression is therefore:
P(1 + 0.021/12)^(12t)
This simplifies to:
P(1.00175)^(12t)
Thus, the second option P(1.00175)^12t is the correct expression representing the amount of money in Stephen's CD investment after t years.