Final answer:
The purchase price of the equipment is calculated using the present value of an annuity formula, incorporating the quarterly payment amount, the number of payments over 7 years, and the adjusted quarterly interest rate of 8%.
Step-by-step explanation:
To calculate the purchase price of the sorting machine that Webster Mining is considering, we need to use the formula for the present value of an annuity because the machine's payments are in the form of a quarterly annuity. Since the payments are $29,600 quarterly for 7 years at an interest rate of 8%, we first need to adjust the interest rate and number of payments to reflect the quarterly periods.
The formula for the present value of an annuity is: PV = Pmt * [(1 - (1 + r) ^-n) / r], where Pmt is the payment amount per period, r is the interest rate per period, and n is the total number of payments.
Here, the quarterly interest rate (r) is 8% divided by 4, which is 2% or 0.02 in decimal form. The total number of quarterly payments (n) is 7 years times 4 quarters, which is 28 payments. Inserting these values into the formula gives us the purchase price of the equipment.
The present value (purchase price) is thus calculated as follows:
PV = $29,600 * [(1 - (1 + 0.02) ^-28) / 0.02]
This calculation will give us the current purchase price of the sorting machine.