The management of a national chain of fast-food outlets is selling a 12 year franchise in a certain city. Past experience in similar localities suggests that t years from now the franchise will be generating profit at the rate of f(t)=10,600 dollars per year. If the prevailing annual interest rate remains fixed at 3% compounded continuously, what is the present value of the franchise?   round answer to nearest penny $

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The management of a national chain of fast-food outlets is selling a 12 year franchise in a certain city and would like to estimate the present value of the franchise based on past data. It is known that the profit generated per year is $10600 and this is true for...

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The management of a national chain of fast-food outlets is selling a 12 year franchise in a certain city and would like to estimate the present value of the franchise based on past data. It is known that the profit generated per year is $10600 and this is true for the entire period of the franchise.

As the rate of interest is 3%, to determine the present value the profit earned in each year has to be discounted at 3%. The present value is the sum of the discounted profit for all the 12 years.

This is equal to `12000/1.03 + 12000/1.03^2 + ... 12000/1.03^12`

= `(12000/1.03)*((1 - 1/1.03^12)/(1 - 1/1.03))`

= 119448.05

The present value of the franchise is $119448.05

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