Question

# Yellow Sand Aviation just bought a new trampoline park. To pay for the trampoline park, the...

Yellow Sand Aviation just bought a new trampoline park. To pay for the trampoline park, the company took out a loan that requires Yellow Sand Aviation to pay the bank a special payment of 5,070 dollars in 4 month(s) and also pay the bank regular payments. The first regular payment is expected to be 1,310 dollars in 1 month and all subsequent regular payments are expected to increase by 0.42 percent per month forever. The interest rate on the loan is 1.62 percent per month. What was the price of the trampoline park?

Solution

Price of trampolin park= Present value of special payment(5070 dollars)+Present value of perpetuity payment

Present value of special payment=Special payment/(1+r)^n

r=discount rate/period=1.62%

n=number of periods=4

Present value of special payment=5070/(1+.0162)^4=4754.35052

Present value of perpetuity payment=Payment made in first month/(r-g)

where first month payment=1310

g=growth rate per period=.42%

r=discounting rate per period=1.62%

Present value of perpetuity payment=1310/(.0162-.0042)

=109166.6667

Thus Price of trampolin park=109166.6667+4754.35052

=113921.0172