Final answer:
To find the present value of lease payments, we use the present value of an annuity due formula involving the payment amount, period interest rate, and total number of payments. Adjustments are made based on whether the compounding is annual or monthly to accurately compute the present value.
Step-by-step explanation:
To calculate the present value of lease payments, we apply the present value formula for an annuity due (since payments are at the beginning of each period) and adjust it based on the compound interest frequency. We'll need to compute this for both annual and monthly compounding scenarios:
Present Value with Annual Compounding
The present value formula for an annuity due is:
PV = Pmt * [(1 - (1 + r)^-n) / r] * (1+r)
Where Pmt is the payment amount ($800), r is the period interest rate (5.75% or 0.0575 annually), and n is the total number of payments (96, since 8 years * 12 months).
However, while the payments are monthly, the compounding is annual, so we first need to adjust the interest rate to the monthly equivalent and use it in the formula.
Present Value with Monthly Compounding
In this scenario, compounding occurs every month, so the formula applies directly with r as 5.75% / 12 and n as 96.
The result will be the sum of the present value of each individual payment at the specified lease rate compounded as per the given frequency.