Caleb deposits $500 in an account that pays him 2% annual interest compounded quarterly. Which equation represents the account balance A after t years?

10

Step-by-step explanation:

500 x 2%

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