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Recitation 11

Recitation 11. Retirement TVM calculations. TVM problems for retirement are really the same as basic annuity and savings/withdrawal problems that we have seen in the past Pay attention to matching the payments and interest rate When do the cash flows start?

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Recitation 11

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  1. Recitation 11

  2. Retirement TVM calculations • TVM problems for retirement are really the same as basic annuity and savings/withdrawal problems that we have seen in the past • Pay attention to matching the payments and interest rate • When do the cash flows start? • Are there separate annuities at play? • Where are the values from the FVA or PVA calculations located at?

  3. Lump Sum Goal • You are 20 years old today and want to have $1,000,000 when you retire. If you can receive 8% annual interest on your funds, how much must you save each year if your first deposit will be one year from now, and your last deposit will be 45 years from now (when you are 65 years old)?

  4. Solution

  5. Savings and Withdrawals • You are forty years old today and you are planning to retire on your 60th birthday. You want to put the same amount of funds aside each year for the next twenty years starting next year so that you will be able to withdraw $50,000 per year for twenty years once you retire, with the first withdrawal occurring on your 61st birthday.. How much must you set aside each year for your retirement if you can earn 10% interest on your money?

  6. Solution

  7. Solution continued • And if we save correctly, the future value of our deposits has to equal the present value of our withdrawals, so we can substitute the PVA above as the FVA for our deposits

  8. How much is left? • You are 25 and decide to save $5,000 every year for the next 40 years for retirement (your first deposit will be 1 year from now). After retiring you withdraw $100,000 every year for 10 years (your first withdrawal is 41 years from now). How much is left of your savings when you are 75 if you can earn an 8% annual interest rate?

  9. Solution

  10. Solution • 65 • 75

  11. Solution Continued

  12. Comparing Plans • You have been given a choice between two retirement policies as described below. • Policy A: You will receive equal annual payments of $20,000 beginning 35 years from now for 10 years. • Policy B: You will receive one lump-sum of $200,000 35 years from now. • Which policy would you choose? Assume the rate of interest is 6.5 percent.

  13. Plan A at t= 44 • A • This sum is at t=44, but the Plan B sum is at t=35. We need to move our value for Plan A to t=35 to be able to make a comparison.

  14. Plan B at t=44 • Now that both sums are located at the same point in time, you would choose Plan B since it is larger than Plan A

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