The initial balance in the account was approximately $4215.

How to find the initial balance in the account?
The formula represents the relationship between the initial balance, the interest rate, the compounding period, and the time period.

To determine the initial balance in the account, we can use the formula for compound interest:

A = P(1 + r)ⁿ

where:

A = the ending balance

P = the initial balance

r = the annual interest rate as a decimal (5% = 0.05)

t = the number of years

Substituting the given values, we get:

5000 = P(1 + 0.05)^((3.5))

5000 = P(1.05)^((3.5))

Dividing both sides by (1.05)^((3.5)), we get:

P = 5000/(1.05)^((3.5))

Using a calculator, we get:

P ≈ $4215

Therefore, the initial balance in the account was approximately $4215.

To find the initial balance (P), we can use the given formula for compound interest:
A = P(1 + r)ⁿ
In this case, we have:
A = $5,000 (ending balance)
r = 0.05 (annual interest rate)
t = 3.5 years (time period)
First, we need to find the number of compounding periods (n). Since the interest is compounded annually and the time period is given in years, n = t = 3.5.
Now, we can plug these values into the formula and solve for P:
$5,000 = P(1 + 0.05)^3.5
To solve for P, we need to isolate it on one side of the equation. First, we can divide both sides by (1 + 0.05)^3.5:
$5,000 / (1 + 0.05)^3.5 = P
Now, we can calculate (1 + 0.05)^3.5:
(1 + 0.05)^3.5 ≈ 1.1806
Next, we can divide $5,000 by this result to find the initial balance (P):
P ≈ $5,000 / 1.1806 ≈ $4,210.74
So, the initial balance in the account was approximately $4,210.74.