Final answer:
To calculate the present value of lease payments at the start of each month for 6 years with annual and monthly compounding at 4.50%, we use the present value of an annuity due formula. The calculation is straightforward for monthly compounding once the monthly rate is determined, while the process for annual compounding requires adjusting the lease rate to match payment frequency.
Step-by-step explanation:
The question asks for the present value of lease payments of $900 made at the beginning of every month for 6 years. We need to find the present value when the lease rate is compounded annually at 4.50% and then when it is compounded monthly at the same rate.
For the lease compounded annually, the formula to use is the present value of an annuity due since payments are made at the beginning of each period. However, since the lease rate is compounded annually, but payments are monthly, we need to adjust the lease rate to match the payment frequency. This becomes quite complex, as finding the equivalent monthly rate that corresponds to the annual compounded rate isn't straightforward and requires an iterative method.
For the lease compounded monthly, the process is more straightforward because the compounding frequency matches the payment frequency. The formula for the present value of an annuity due can be used directly, taking into account the monthly interest rate and the total number of payments.
To calculate the present value, the monthly rate (when compounded monthly) is found by dividing the annual rate by 12. The present value formula is generally:
PV = Pmt * [(1 - (1 + r)^(-n)) / r] * (1+r)
where PV is the present value, Pmt is the lease payment of $900, r is the monthly interest rate, and n is the total number of payments (72 months for 6 years).