Need help with questions 4 and 5.
Project 1 In this project, you play the role of a financial advisor. In particular, you will advise a client regarding her annuities. Let f(t) represent the rate of payment (income received) in dollars per year at time t. Income received at a rate of f(t) over a time period is called an annuity (or income stream). The future value, FV, of a present value, PV, compounded continuously, at an annual percentage rate, APR, of r, for t years is FV = PVert 1. The formula for the future value of an annuity over time period [0, 7] is given by FV = 5"er(t). f(t)dt. If your client intends to contribute $250 per month for 35 years with a 9% rate of return, then find the future value of your client's annuity. 2. The present value (the amount you need to have now in order to make future payments of a given amount) of an annuity is the current value of a series of payments to be made at specified future times for a specified time period, given some rate of return, r, on the annuity principal during the time period. The formula for the present value is FV = 5"e-t. f (t)dt. If your client already has an annuity that is invested at 6% APR, and she needs the annuity to pay out $1000 per month for 20 years then find the present value of that annuity. 3. Contributions to an annuity are usually a percentage of your salary, and rates of return vary. Referring to Question 1, consider your client's $250 per month contribution, increased by 5% per year for 35 years at 8%, compounded continuously. What will then be the value of the annuity? 4. Upon retirement, your client invests the amount from Question 3 in a secure investment earning a fixed rate of return of 6%, compounded continuously. If she wants her annuity to last for exactly 25 years then what constant monthly payment amount should you recommend that she draw off? 5. Based on your work, suggest an investment plan for your client that will maximize her retirement income. Your suggestions should be specific as to her expected income with any appropriate calculations. Project 1 In this project, you play the role of a financial advisor. In particular, you will advise a client regarding her annuities. Let f(t) represent the rate of payment (income received) in dollars per year at time t. Income received at a rate of f(t) over a time period is called an annuity (or income stream). The future value, FV, of a present value, PV, compounded continuously, at an annual percentage rate, APR, of r, for t years is FV = PVert 1. The formula for the future value of an annuity over time period [0, 7] is given by FV = 5"er(t). f(t)dt. If your client intends to contribute $250 per month for 35 years with a 9% rate of return, then find the future value of your client's annuity. 2. The present value (the amount you need to have now in order to make future payments of a given amount) of an annuity is the current value of a series of payments to be made at specified future times for a specified time period, given some rate of return, r, on the annuity principal during the time period. The formula for the present value is FV = 5"e-t. f (t)dt. If your client already has an annuity that is invested at 6% APR, and she needs the annuity to pay out $1000 per month for 20 years then find the present value of that annuity. 3. Contributions to an annuity are usually a percentage of your salary, and rates of return vary. Referring to Question 1, consider your client's $250 per month contribution, increased by 5% per year for 35 years at 8%, compounded continuously. What will then be the value of the annuity? 4. Upon retirement, your client invests the amount from Question 3 in a secure investment earning a fixed rate of return of 6%, compounded continuously. If she wants her annuity to last for exactly 25 years then what constant monthly payment amount should you recommend that she draw off? 5. Based on your work, suggest an investment plan for your client that will maximize her retirement income. Your suggestions should be specific as to her expected income with any appropriate calculations
