Final answer:
The question seeks the nominal interest rate for a 7 year lease with monthly payments made at the beginning of the month. The present value annuity due formula is used to calculate this interest rate, which requires numerical methods or a financial calculator.
Step-by-step explanation:
The question asks to determine the nominal interest rate compounded monthly for a 7 year lease with an upfront value of $39,700 and monthly payments of $500 made at the beginning of each month.
To solve this, we use the formula for the present value of an annuity due, because payments are made at the beginning of each period. Given:
PV = present value of the annuity ($39,700),
PMT = payment per period ($500),
n = total number of payments (7 years * 12 months/year = 84 payments),
i = periodic interest rate,
we need to find the monthly interest rate that satisfies the equation:
PV = PMT * ((1 - (1 + i)^-n) / i) * (1 + i).
The equation cannot be solved algebraically and requires financial calculator or numerical methods such as Newton-Raphson or Excel's RATE function to find the interest rate to two decimal places.