A 60-year-old couple is considering opening a business of their own. They will either purchase an established Gift and Card Shoppe or open a new Wine Boutique. The Gift Shoppe has a continuous income stream with an annual rate of flow at time t given by G(t) = 34,000 (dollars per year). The Wine Boutique has a continuous income stream with a projected annual rate of flow at time t given by W(t) = 21,900e0.08t (dollars per year). The initial investment is the same for both businesses, and money is worth 10% compounded continuously. Find the present value of each business over the next 5 years (until the couple reaches age 65) to see which is the better buy. (Round your answers to the nearest dollar.)

Question

A 60-year-old couple is considering opening a business of their own. They will either purchase an established Gift and Card Shoppe or open a new Wine Boutique. The Gift Shoppe has a continuous income stream with an annual rate of flow at time t given by

G(t) = 34,000 (dollars per year).

The Wine Boutique has a continuous income stream with a projected annual rate of flow at time t given by

W(t) = 21,900e^0.08t (dollars per year).

The initial investment is the same for both businesses, and money is worth 10% compounded continuously. Find the present value of each business over the next 5 years (until the couple reaches age 65) to see which is the better buy. (Round your answers to the nearest dollar.)