Assume the total cost for invest in a business will be $280,000 in 18 years. You presently have $45,000 to invest. What annual rate of interest must you earn on your investment to cover the cost?

To solve this problem, we will use the formula for compound interest, which is:

A = P(1 + r/n)^(nt)

Where: A = the amount of money accumulated after n years, including interest. P = the principal amount (the initial amount of money) r = annual interest rate (in decimal) n = number of times that interest is compounded per year t = time the money is invested for in years

In this case, we are trying to find the annual interest rate (r), so we will need to rearrange the formula to solve for r.

Given: A = $280,000 (the amount of money you want to have in 18 years) P =$45,000 (the amount of money you currently have to invest) n = 1 (since we are looking for an annual interest rate, we will assume the interest is compounded once per year) t = 18 years

Substituting the given values into the formula, we get:

$280,000 =$45,000(1 + r/1)^(1*18)

Solving for r:

1 + r = ($280,000 /$45,000)^(1/18) r = (($280,000 /$45,000)^(1/18)) - 1

Now, calculate the right side of the equation to find the value of r. This will give you the annual interest rate you need to earn on your investment to have $280,000 in 18 years.