Answer:
The answer is A = 500 * (1 + 0.005)^4t
Step-by-step explanation:
1. Let's review the information given to us to answer the question properly:
Initial deposit = $ 500
Interest rate = 2% = 0.02/4 = annual compounded quarterly
2. Which equation represents the account balance A after t years?
Let's write the equation to answer the question, this way:
Account balance = Initial deposit * (1 + r)^4t
Replacing with the values we already know, we have:
A = 500 * (1 + 0.005)^4t
Where:
A = Account balance
0.005 = Interest rate per quarter = 0.02/4
4t = Number of quarters (4 * Number of t years)
The answer is A = 500 * (1 + 0.005)^4t
Suppose we want to calculate the account balance after 4.5 years, then we substitute this way:
A = 500 * (1 + 0.005)^4.5*4
A = 500 * (1 + 0.005)¹⁸
A = 500 * 1.094
A = 547
After 4.5 years or 18 quarters, the account balance is $ 547
