Problem 2: Continuous Income Stream Problem 2 Suppose you are interested in saving for retirement. Right now, you are only able to invest $500 per year. Each subsequent year, you will invest $400 more than the year before thanks to your increasing wages. We can represent this as a continuous income stream function: F(t) = 400t + 500 For simplicity, you choose to invest in an index fund that tracks the S&P 500. Based on historical information, you anticipate this fund to have an average rate of return of about 10% annually. Assuming continuous compounding and using the continuous income stream formula, approximate the future value after 30 years of investing. To do this, complete the following steps: a. Find the present value of this investment using integration. Note that the integral will require integration by parts. Be sure to show each step of the calculation carefully and round your result to the nearest cent. b. Using the present value, find the future value using the compound interest formula. Round your result to the nearest cent. Side note: we are making a lot of strong assumptions to do this calculation. If you are interested in a better estimate, you can play with the following investment calculator. Problem 2: Continuous Income Stream Problem 2 Suppose you are interested in saving for retirement. Right now, you are only able to invest $500 per year. Each subsequent year, you will invest $400 more than the year before thanks to your increasing wages. We can represent this as a continuous income stream function: F(t) = 400t + 500 For simplicity, you choose to invest in an index fund that tracks the S&P 500. Based on historical information, you anticipate this fund to have an average rate of return of about 10% annually. Assuming continuous compounding and using the continuous income stream formula, approximate the future value after 30 years of investing. To do this, complete the following steps: a. Find the present value of this investment using integration. Note that the integral will require integration by parts. Be sure to show each step of the calculation carefully and round your result to the nearest cent. b. Using the present value, find the future value using the compound interest formula. Round your result to the nearest cent. Side note: we are making a lot of strong assumptions to do this calculation. If you are interested in a better estimate, you can play with the following investment calculator