Question

# An entrepreneur is looking to purchase an office building. She will make quarterly payments at the...

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?

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

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