A firm purchased a 16-year franchise for a computer outlet store that is expected to generate income at the rate of dollars per year.If the prevailing interest rate is 10% per year compounded continuously, find the present value of the franchise.
A)$1,114,979
B)$2,250,532
C)$4,660,006
D)$3,192,414
E)$1,756,632

Question

A firm purchased a 16-year franchise for a computer outlet store that is expected to generate income at the rate of  dollars per year.If the prevailing interest rate is 10% per year compounded continuously, find the present value of the franchise.
A)$1,114,979 
B)$2,250,532 
C)$4,660,006 
D)$3,192,414 
E)$1,756,632

Quizplus · Accepted Answer

The present value of the franchise can be found using the continuous compounding formula: PV = FV/e^(rt), where FV is the future value (income at the end of 16 years), r is the interest rate, and t is the time in years. 
In this problem, FV = 11eb12b0_a961_1d03_b394_cb619b5adfaf_TB7866_11 dollars, r = 0.1 (10% per year), and t = 16. 
Plugging these values into the formula gives:
PV = 11eb12b0_a961_1d03_b394_cb619b5adfaf_TB7866_11/e^(0.1*16) 
Using a calculator, we get: 
PV = $3,192,414.48
Therefore, the best choice is (D), $3,192,414.

A Firm Purchased a 16-Year Franchise for a Computer Outlet