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You are currently 32 years old and have managed to save a total of $110,000 towards your retirement, which will happen at the end of the year in which you turn 65 years of age (33 years from now). In addition, you have just won a lottery prize in the amount of $75,000.

Your retirement plans include retiring in luxury for 15 years, after which you will move into a retirement residence for 10 years, and then you will exit gracefully from your life. You have estimated the cost of your luxury retirement to be $12,000 per month, and the cost of the retirement residence is estimated to be $4,500 per month. It is also your plan to leave $100,000 to the local library and arts centre upon your death. Assume an interest rate of 2.50% unless indicated otherwise.

Round all amounts to two (2) decimal places

a)How much money will you need to have in your retirement fund when you retire in order to fund your retirement plans? You will not be making any payment towards your retirement fund once you retire. (7 marks)

b)Given your answer in part a) and the funds you currently have on hand, how much must you contribute each month to your retirement fund to meet your retirement goal?

c)Assume now that you believe that between now and when you retire you expect interest rates to be 3.75% and then remain at 2.50% during your retirement. What is the new amount of your monthly contribution to your retirement fund?

d)Assume now that you believe that between now and when you retire you expect interest rates to be 3.75% for the next 15 years, then 3.0% for the remaining years until you retire, and then remain at 2.50% during your retirement. In addition, you expect to receive $100,000 inheritance 5 years from now. What is the new amount of your monthly contribution to your retirement fund?

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