Final answer:
Using the simple interest formula, and rearranging it to solve for principal, Joey's initial deposit was calculated to be approximately $2,222.22 after he earned $400 in interest over 3 years at a 6% interest rate.
Step-by-step explanation:
To find Joey's initial deposit amount, we first need to understand the formula for calculating simple interest.
The formula for simple interest is I = P × r × t, where I is the interest earned, P is the principal amount (initial deposit), r is the annual interest rate (in decimal form), and t is the time in years the money is deposited for.
In Joey's case, he earned $400 in interest over 3 years at a rate of 6%.
Thus, we can rearrange the simple interest formula to solve for the principal P: P = I / (r × t). Plugging in the numbers, we get:
P = $400 / (0.06 × 3) = $400 / 0.18 = $2,222.22 (approximately)
Therefore, Joey's initial deposit was approximately $2,222.22.