A 58-year-old couple are considering opening a business of their own. They will either purchase an established Gift and Card Shoppe or open a new Video Rental Palace. The Gift Shoppe has a continuous income stream with an annual rate of flow at time t given by (dollars per year) and the Video Palace has a continuous income stream with a projected annual rate of flow at time t given by (dollars per year). The initial investment is the same for both businesses, and money is worth 10% compounded continuously. Determine which is the better buy by finding the present value of each business over the next 6 years (until the couple reach age 64).
A) the Video Palace
B) the Gift Shoppe

Question

A 58-year-old couple are considering opening a business of their own. They will either purchase an established Gift and Card Shoppe or open a new Video Rental Palace. The Gift Shoppe has a continuous income stream with an annual rate of flow at time t given by  (dollars per year) and the Video Palace has a continuous income stream with a projected annual rate of flow at time t given by  (dollars per year). The initial investment is the same for both businesses, and money is worth 10% compounded continuously. Determine which is the better buy by finding the present value of each business over the next 6 years (until the couple reach age 64). ​
A) the Video Palace 
B) the Gift Shoppe

Quizplus · Accepted Answer

The Answer of A 58-year-old couple are considering opening a business of their own. They will either purchase an established Gift and Card Shoppe or open a new Video Rental Palace. The Gift Shoppe has a continuous income stream with an annual rate of flow at time t given by  (dollars per year) and the Video Palace has a continuous income stream with a projected annual rate of flow at time t given by  (dollars per year). The initial investment is the same for both businesses, and money is worth 10% compounded continuously. Determine which is the better buy by finding the present value of each business over the next 6 years (until the couple reach age 64). ​
A) the Video Palace 
B) the Gift Shoppe

A 58-Year-Old Couple Are Considering Opening a Business of Their