If the couple in Problem plan to keep the business until age 70 (for the next 12 years), find each present value to see which business is the better buy in this case.
Problem
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 Wine Boutique.
The Gift Shoppe has a continuous income stream with an annual rate of flow at time t given by G(t) = 30,000 (dollars per year) and the Wine Boutique has a continuous income stream with a projected annual rate of flow at time t given by W(t) = 21,600e0.08t (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 7 years (until the couple reach age 65) to see which is the better buy.