Final answer:
To calculate the annual rental for the small aircraft, use the present value of an annuity formula. With a cost of $900,000 and a desired return of 10% over twenty years, the annual rental would be approximately $94,000.
Step-by-step explanation:
To calculate the annual rental for the small aircraft, we need to determine the present value of the future lease payments. In this case, the lease payments are annual and made at the end of each year for twenty years. The cost of the aircraft is $900,000 and Jeremy wants to earn a return of 10%. Using the formula for the present value of an annuity, we can calculate the annual rental:
PV = PMT * ((1 - (1 + r)^-n) / r)
Where:
PV = Present Value
PMT = Payment amount per period
r = Interest rate per period
n = Number of periods
Plugging in the values, we get:
PV = PMT * ((1 - (1 + 0.1)^-20) / 0.1)
Solving for PMT, we find:
PMT = PV / ((1 - (1 + 0.1)^-20) / 0.1)
Substituting the values:
PMT = $900,000 / ((1 - (1.1)^-20) / 0.1)
PMT = $900,000 / (9.563)
PMT ≈ $94,000
Therefore, the annual rental that Jeremy should charge for the small aircraft to earn a return of 10% is approximately $94,000.