Final answer:
The present value of a lease contract with payments of $800 per month for 5 years is computed using an annuity due formula, differing based on the compounding period - annually or monthly. Annual compounding requires converting to a monthly rate, whereas the monthly compounding uses the monthly rate directly in calculations.
Step-by-step explanation:
To calculate the present value of the contract with lease payments of $800 at the beginning of every month for 5 years, we need to consider the lease rate and the compounding period.
Present Value with Annual Compounding
For an interest rate of 3.50% compounded annually, we use the formula for the present value of an annuity due (payments at the beginning of the period), considering the compounding occurs less frequently than the payments:
PV = Pmt * [(1 - (1 + r)^-n) / r] * (1 + r)
In this case, we convert the annual interest rate to a monthly equivalent, assuming each year has 12 months, and then compute the present value of monthly payments across 60 months (5 years).
Present Value with Monthly Compounding
For a lease rate of 3.50% compounded monthly, we use the same annuity due formula but with the monthly compounding rate directly:
PV = Pmt * [(1 - (1 + r)^-n) / r] * (1 + r)
Here, 'r' is the monthly interest rate (annual rate divided by 12) and 'n' is the total number of payments (5 years x 12 months).