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**

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