Bridges INCOME STREAMS Math 115bEXAMPLE 1:The Plastic-Is-Us Toy Company considers its incoming revenue as an income stream, rather than as a huge collection of discrete payments. At a time t years from the start of its fiscal year on July 1, the company expects to receive revenue at the rate of A(t) million dollars per year. Records from past years indicate that Plastic-Is-Us can model its revenue rate with A(t) = -110×t5 + 330×t4 - 330×t3 + 110×t2 +3.174 million dollars per year.(a) Calculate the total amount of revenue that the company will receive in one year by integrating A(t) from 0 years to 1 year. Total Revenue=∫0TA(t)dtRecall that A dollars, invested for t years at an annual rate r, compounded continuously, has a present value P= A e−rt. Similarly, an income stream of A (t ) dollars per year, startingnow and continuing for the next T years is given by Present Value =∫0TA(t)∙ e−rtdt.(b) Calculate the present value of this income stream during the next year.EXAMPLE 2:Let A(t)=$ 950,000 be the constant income stream per year for the next three years at 6% compounded continuously.(a) Calculate the present value of this constant income stream for the next three years.(b) Calculate the total revenue that will be made during the three year period.Bridges INCOME STREAMS Math
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