How much was invested if the future value of the investment is $7,083.34 and the interest was at 4% compounded quarterly for a period of 3.5 years?

To find out how much was invested, we need to use the formula for the future value of a compound interest investment, which is:

FV = PV * (1 + r/n)^(nt)

Where: FV = Future Value PV = Present Value (the initial amount of money) r = annual interest rate (in decimal form) n = number of times that interest is compounded per year t = time the money is invested for in years

We can rearrange this formula to solve for the present value (PV), which is the amount that was initially invested:

PV = FV / (1 + r/n)^(nt)

Given in the problem: FV = $7,083.34 r = 4% = 0.04 (in decimal form) n = 4 (since interest is compounded quarterly) t = 3.5 years

Substituting these values into the formula gives:

PV = $7,083.34 / (1 + 0.04/4)^(4*3.5)

Now, we just need to calculate the right-hand side of this equation.

First, calculate the value inside the parentheses:

1 + 0.04/4 = 1.01

Then, raise this to the power of (4*3.5):

(1.01)^(4*3.5) = 1.144409

Finally, divide the future value by this number:

$7,083.34 / 1.144409 =$6,188.96

So, the initial investment was approximately $6,188.96.