To find out how much the investment earned in the fourth year, let's work through the problem step by step.
Let's assume that the amount of money invested in the business in the first year is x dollars. According to the problem, in each subsequent year, the investment earns 1 1/2 times as much as the preceding year.
So, in the first year, the investment earns x dollars.
In the second year, it earns (1 1/2) * x = (3/2) * x dollars.
In the third year, it earns (1 1/2) * (3/2) * x = (9/4) * x dollars.
And in the fourth year, it earns (1 1/2) * (9/4) * x = (27/8) * x dollars.
Now, let's set up an equation to represent the total earnings over the four years. We know that the total earnings over the four years is $29,250.00.
So, we have the following equation:
x + (3/2)x + (9/4)x + (27/8)x = 29,250
To simplify the equation, we need to find a common denominator for the fractions on the left side:
8x/8 + 12x/8 + 18x/8 + 27x/8 = 29,250
Combine the terms on the left side:
(65x/8) = 29,250
To solve for x, multiply both sides by 8/65:
x = (29,250 * (8/65))
Calculating this, we find:
x ≈ $3,600.00
Now, to find the earnings in the fourth year, we substitute x back into the equation:
(27/8) * $3,600.00 ≈ $12,150.00
Therefore, the investment earned approximately $12,150.00 in the fourth year.