(Solved): Math 0130 Tutorial 9: Comparing Investments Two students are saving money for a graduation trip to ...

Math 0130 Tutorial 9: Comparing Investments Two students are saving money for a graduation trip to Europe in several years. George has just sold his car for \( \$ 5000 \) and has invested his money in a fund at an interest rate of \( 5.4 \% \) per year, compounded monthly. At the same time, John has invested his part-time job savings of \( \$ 4500 \) in another fund at an interest rate of \( 6.8 \% \) per year, compounded quarterly. a. Using the compound interest formula (see page 290), find an exponential growth model for the money belonging to each student. Start by filling in the following table to specify the parameters \( \mathrm{P} \), \( r \), and \( n \) for each investment. Then find the exponential model for each investment, approximating the base to 4 decimal places. b. i) Calculate the future value of each investment after 4 years to the nearest dollar. ii) Using DESMOS, sketch both exponential growth curves on the practical domain on the same Cartesian Plane. From the graph, confirm the value of each imvestment after 4 years and find the approximate time for the investments to be equal in value. c. i) If the investment is left in place, algebraically determine the time for George's investment to double, Find an exact answer in terms of base e and then use a calculator to find a decimal approximation to the nearest year. Check with the DESMOS graph.