Lease-A-Rama Co. leases equipment to Dunlavy Co. over a lease term of 5 years, with equal annual payments starting the first day of the lease. The fair value of the equipment is $500,000 and the expected residual value at the end of the lease term is $50,000. Lease-A-Rama expects a 12% return on investment as a result of the lease. What is the amount of the equal lease payments Dunlavy will make, and at what amount will Lease-A-Rama record its gross investment in the lease?

Hi, in order to find the annuity of a lease that has a 12% return and residual value of $50,000, for four years and with its first payment made the same day of the lease, we need to solve for "A" the following equation.

[tex]PresentValue=A+\frac{A((1+r)^{n-1}-1) }{r(1+r)^{n-1} } +\frac{ResidualValue}{(1+r)^{n} }[/tex]

Where:

r= expected rate of return

n= Number of payments

Therefore, everything should look like this

[tex]500,000=A+\frac{A((1+0.12)^{4}-1) }{0.12(1+0.12)^{4} } +\frac{50,000}{(1+0.12)^{5} }[/tex]

[tex]500,000=A+A(3.03734935)+28,371.34[/tex]

[tex]500,000-28,371.34=A(4.03734935)[/tex]

[tex]\frac{500,000-28,371.34}{4.03734935} =A[/tex]

[tex]A=116,816.41[/tex]

That is the annual payment of the lease, with a residual value of 50,000, rate = 12%, for 5 years, with its first payment made the same day that the lease was issued.

B) the gross invesment to be recorded by Lease-A-Rama is

116,816.41*5 + 50,000= 634,082.05

Best of luck.