Final answer:
The list price of the equipment can be found by calculating the present value of the annuity due for the lease payments and adding the down payment. This is done using the present value of an annuity due formula adjusted to quarterly payments and a monthly compounded interest rate.
Step-by-step explanation:
To calculate the list price of the equipment leased under the given terms, we should use the present value of an annuity due formula. The lease requires quarterly payments of 417 over 90 months, at an interest rate compounded monthly.
To find the present value (PV) of the total payments, we first convert the interest rate to a quarterly rate, because payments are made quarterly, not monthly. The monthly rate is 7.28% per year, or approximately 0.607% per month (7.28 divided by 12). The quarterly rate is then approximately three times the monthly rate (3 times 0.607%), because there are three months in a quarter.
We can now calculate the present value of the annuity due using the formula:
PV = P × ╠├1 - (1 + r)^-n╯ / r╣ × (1 + r)
where P is the periodic payment (417), r is the quarterly interest rate (converted from the annual rate), and n is the total number of payments (90 months / 3 months per quarter).
After finding the present value of the annuity due, we add the 2000 down payment to this present value, which gives us the total list price of the equipment.
Finally, we adjust all calculations to two decimal places as instructed