9. (8 points). An Investment Problem. Mr and Mrs. Future Planners, during their next month when they turn 25 years of age start investing for their retirement. They initially invest $1,000 in a portfolio of some fundamental stocks which return continuously (in average) at annual percentage rate APR = 6% continuously. In addition, they plan to deposit $6000 increased at inflation rate of 3% every year. Namely, they increase it to next year, then to in year 2, etc. i.e. S6000 The couple consider that when they turn 65 years old, when they will be ready to retire, they stop depositing money, move their invested money in a more conservative portfolio of some mutual funds which returns in average at fixed rate APR = 5% compounded continuously; and continuously withdraw $70,000 per year. This amount in addition to their social security benefits will be adequate to enjoy continuing their life style and have happy retirement. They also promise to take care of their health by exercising well and eating healthy, thus, they should be in good shape financially and physically to enjoy happy life during their retirement. 1. Write an initial value problem that models the problem during their working years. II. Solve the initial value problem found above to find the function S(1), which gives the account balance at any timet III Graph the function found above. IV. Find the balance of the account at 40 years later, when they are ready to retire. V. Find the total amount that they deposited into the account in entire 40 years of investment VI. Write an initial value problem that models the problem during their retirement years. VII Find the balance of their account at their age 90. 9. (8 points). An Investment Problem. Mr and Mrs. Future Planners, during their next month when they turn 25 years of age start investing for their retirement. They initially invest $1,000 in a portfolio of some fundamental stocks which return continuously (in average) at annual percentage rate APR = 6% continuously. In addition, they plan to deposit $6000 increased at inflation rate of 3% every year. Namely, they increase it to next year, then to in year 2, etc. i.e. S6000 The couple consider that when they turn 65 years old, when they will be ready to retire, they stop depositing money, move their invested money in a more conservative portfolio of some mutual funds which returns in average at fixed rate APR = 5% compounded continuously; and continuously withdraw $70,000 per year. This amount in addition to their social security benefits will be adequate to enjoy continuing their life style and have happy retirement. They also promise to take care of their health by exercising well and eating healthy, thus, they should be in good shape financially and physically to enjoy happy life during their retirement. 1. Write an initial value problem that models the problem during their working years. II. Solve the initial value problem found above to find the function S(1), which gives the account balance at any timet III Graph the function found above. IV. Find the balance of the account at 40 years later, when they are ready to retire. V. Find the total amount that they deposited into the account in entire 40 years of investment VI. Write an initial value problem that models the problem during their retirement years. VII Find the balance of their account at their age 90. 9. (8 points). An Investment Problem. Mr and Mrs. Future Planners, during their next month when they turn 25 years of age start investing for their retirement. They initially invest $1,000 in a portfolio of some fundamental stocks which return continuously (in average) at annual percentage rate APR = 6% continuously. In addition, they plan to deposit $6000 increased at inflation rate of 3% every year. Namely, they increase it to next year, then to in year 2, etc. i.e. S6000 The couple consider that when they turn 65 years old, when they will be ready to retire, they stop depositing money, move their invested money in a more conservative portfolio of some mutual funds which returns in average at fixed rate APR = 5% compounded continuously; and continuously withdraw $70,000 per year. This amount in addition to their social security benefits will be adequate to enjoy continuing their life style and have happy retirement. They also promise to take care of their health by exercising well and eating healthy, thus, they should be in good shape financially and physically to enjoy happy life during their retirement. 1. Write an initial value problem that models the problem during their working years. II. Solve the initial value problem found above to find the function S(1), which gives the account balance at any timet III Graph the function found above. IV. Find the balance of the account at 40 years later, when they are ready to retire. V. Find the total amount that they deposited into the account in entire 40 years of investment VI. Write an initial value problem that models the problem during their retirement years. VII Find the balance of their account at their age 90. 9. (8 points). An Investment Problem. Mr and Mrs. Future Planners, during their next month when they turn 25 years of age start investing for their retirement. They initially invest $1,000 in a portfolio of some fundamental stocks which return continuously (in average) at annual percentage rate APR = 6% continuously. In addition, they plan to deposit $6000 increased at inflation rate of 3% every year. Namely, they increase it to next year, then to in year 2, etc. i.e. S6000 The couple consider that when they turn 65 years old, when they will be ready to retire, they stop depositing money, move their invested money in a more conservative portfolio of some mutual funds which returns in average at fixed rate APR = 5% compounded continuously; and continuously withdraw $70,000 per year. This amount in addition to their social security benefits will be adequate to enjoy continuing their life style and have happy retirement. They also promise to take care of their health by exercising well and eating healthy, thus, they should be in good shape financially and physically to enjoy happy life during their retirement. 1. Write an initial value problem that models the problem during their working years. II. Solve the initial value problem found above to find the function S(1), which gives the account balance at any timet III Graph the function found above. IV. Find the balance of the account at 40 years later, when they are ready to retire. V. Find the total amount that they deposited into the account in entire 40 years of investment VI. Write an initial value problem that models the problem during their retirement years. VII Find the balance of their account at their age 90