Question

An entrepreneur is looking to purchase an office building. She will make quarterly payments at the beginning of the month. Her first payment will be $1000, and each subsequent payment will increase by 20%. (That is, the second payment is $1,200, and the third payment is $1,440, and so on.) The loan will last 8 years. If the APR is 14%, how much did the office building cost?

Answer 1

Quarterly Payment at the beginning of the Month = $1000

Growth rate in each subsequent payment = 20%

Calculating the Present Value of the Payments today using Present Value of Growth annuity due formula:-

Where, C= Periodic Payments = $1,000

r = Periodic Interest rate = 14%/4 = 3.5% (As quarterly Payments)

g = Growth rate of Payments = 20%

n= no of periods = 8 years*4 = 32

Present Value = $706,851.33

So, Office Building Cost is $706,851.33