urgent need help/don’t understand (investment theory question–>finance)
You intend to develop a retirement plan for yourself. After graduation from UBC, you expect to and a well paying job and start actively saving for your retirement at the age of 25 years old. You expect to retire at 65 years old and you want to have at least $60,000 a year for 25 years of your retirement. (Let’s assume you expect to live independently till 90 years old and afterwards you plan to move in with your children and make it their responsibility to support you.)
(a) How much money will you need to have in your retirement account when you turn 65 years old if you intend to have the above-described quality of life during your retirement? Assume that you will make exactly 25 annual withdrawals from your retirement account and you will make the first one right after your 65th birthday. Also, assume that your retirement account will be paying at at monthly APR of 3.5% after you reach 65 years.
(b) Let’s denote the amount of money you found in part (a) as x. How much money do you need to put into your retirement account at the age of 25 years as a lump sum to have $x when you turn 65 years old? Assume that the money will stay there for 40 years and it will earn a quarterly APR of 4.5% over those 40 years.
(c) You realize that you cannot afford the lump sum payment. So you decide to contribute to your retirement account every year for 40 years, i.e. to make 40 contributions. How much do you need to contribute every year to have $x when you turn 65 years old? Assume a quarterly APR of 4.5%.
(d) Now you are deciding whether to open an RRSP account (Registered Retirement Savings Plan) or a standard savings account. If you open an RRSP account, all the tax payments are deferred and you will pay 28% tax1 when you withdraw the money during your retirement. If you still want to receive each year $60,000 after tax, how much money do you need to have in you retirement account at the age of 65? Compare your answer to the one you obtained in part (a). How much money do you need to contribute each year? Compare your answer to the one you obtained in part (c).
(e) If you open a savings account, you will pay income taxes at the end of each year on the interest accumulated within a given year. Assume an income tax of 15%, which means that the effective interest rate you will earn on all your investments will be lower by 15%. For example, instead of the EAR of 4.577%, you will earn 3.890%. How much money do you need to have in you retirement account at the age of 65? Compare your answer to the one you obtained in part (a). How much money do you need to contribute each year? Compare your answer
to the one you obtained in part (c).