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(a) Find the present and future value of an income stream of $5000 per year for a period of 10 years if the interest rate, compounded continuously, is 5%. Round your answers to two decimal places. Presentvalue =$ Futurevalue =$ (b) How much of the future value is from the income stream? How much is from interest? Round your answers to two decimal places. The amount from the income stream is S The amount from the interest is $ A recently installed machine earns the company revenue at a continuous rate of 60,000r+45,000 dollars per year during the first six months of operation and at the continuous rate of 75.000 dollars per year after the first six months. The cost of the machine is $169,000, the interest rate is 7% per year, compounded continuously, and r is time in years since the machine was installed. (a) Find the present value of the revenue earned by the machine during the first year of operation. Round your answer to the nearestinteger. (b) Find how long it will take for the machine to pay for itself; that is, how long it will take for the present value of the revenue to equal the cost of the machine? Round your answer to two decimal places. years (a) An investment account earns 10% interest compounded continuously. At what (constant, continuous) ray must a parent deposit money into such an account in order to save $100,000 in 9 years for a child's college expenses? Give the result in dollars per year. Round your answer to the nearest dollar. Anannuity makes annual payments of $41.000 startingnow, from an account paying 3.65 of interest peryear, compounded annually. Round your answers to two decimal places. (a) Find the present value of the annuity if it makes ten payments. Present value of annuity =$ (b) Find the present value of the annulty if it makes payments in perpetuity. Present value of annuity m5