To calculate the amount of money that needs to be set aside today to purchase a new piece of equipment in 3 years, we need to find the future value of the equipment and calculate the present value of that future amount.
First, let's find the future value of the equipment:
The cost of the equipment is expected to increase by 3% per year, so after 3 years the cost will be:
$75,000 * (1 + 0.03)^3 = $78,225
Next, let's find the present value of that future amount:
The money is expected to earn 9% interest compounded annually, so to find the present value, we need to discount the future amount by the interest rate. We can use the formula:
PV = FV / (1 + r)^t
where PV is the present value, FV is the future value, r is the interest rate, and t is the number of years.
Plugging in the values, we get:
PV = $78,225 / (1 + 0.09)^3 = $73,232.57
So, to purchase the equipment in 3 years, we need to set aside $73,232.57 today.