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## Section 5.4

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**Section 5.4**Annuities (Retirement Funds) Alaysia 5.4 Retirement Funds**1 of 30**I see how investing in a retirement fund is an example of recursion • Absolutely • Sort of • Not a clue Explain: 5.4 Retirement Funds**1 of 30**Educated Guess **Alaysia, who is 25 years old, plans to retire at age 65. She contributes $1000 annually at 10% interest. How much will she have when she retires? • $40,000 • $80,015 • $120,565 • $442,593 5.4 Retirement Funds**1 of 30**What is the total amount that Alaysia will deposit in her account until she retires? • $40,000 • $60,000 • $80,000 5.4 Retirement Funds**1 of 30**Which recursion formula calculates Alaysia’s balance? • Ans + .10*Ans - 1000 • Ans + .10*Ans + 1000 • Ans - .10*Ans - 1000 • Ans - .10*Ans + 1000 5.4 Retirement Funds**“Alaysia” $1000/year 10%**Age 25 $0 Age 26 $1,000 Age 27 In general, 6 5.4 Retirement Funds**1 of 30**How much Alaysia will have if she takes an early retirement at 55? (Ans) • $40,000 • $80,015 • $120,565 • $442,593 ? + + = $0 Age 25 10% + $1,000 Age 55 5.4 Retirement Funds**$**Years $ Years $ Years $ Years 1 of 30 “Alaysia” Which graph best describes the growth of Alaysia’s retirement fund? • . • . • . • 1 • 2 • 3 • 4 5.4 Retirement Funds**1 of 30**You invest $500 at the end of each month in an account paying 5% interest. To find your balance at the end of two years you type in 500 Ans + 5*500 + 1000How many errors did you make? • 1 • 2 • 3 • 4 or more 5.4 Retirement Funds**Annuities (APPS)**N Number of payments made –years I% Annual interest rate –%, not a decimal PV 0 PMT Your periodic payment – as a negative (-) FV Value of the account after N payments P/Y Number of payments per year C/Y Number of compoundings per year 10 5.4 Retirement Funds**13 of 30**Using APPS verify that Alaysia will have $442,493 ? + + = $0 10% $1,000 Age 65 N = I% = PV = PMT = FV = P/Y = C/Y = 5.4 Retirement Funds**Volatility: Stock Market Returns Fluctuate from Year to Year**S&P 500 Total Return Source: Bloomberg 12 5.4 Retirement Funds**From 1990 - 1999, the average stock fund gained 23.6% per**year. $10,000 invested grew to $83,194 • The top 5 funds for the 10 years ending June 2000 all had quarters where they pulled back sharply with a 25% or more loss for the quarter • “Timing the Market” - Frequent jumping from one fund to another - is a big mistake. 13 5.4 Retirement Funds**1 of 30**Alaysia and Rhona begin work at age 25. Each will invest $1,000 at the end of each year until they are both 65. Alaysia gets 10% interest; Rhona gets 11%. How much more will Rhona have in her account after they have made their last payment at age 65? • $97,445 • $103,919 • $135,867 • $139,233 5.4 Retirement Funds**Rule 1**A slightly higher interest rate can earn substantially more money in the long run 15 5.4 Retirement Funds**16**5.4 Retirement Funds**Rule 2**Small payments over time can earn huge amounts of money 17 5.4 Retirement Funds**8%**$4.50 1 of 30 “Jill - Cigarettes” $4.50 per pack • $1,166 • $48,297 • $482,976 • $4,829,757 Daily ? + + = Age 60 $0 age 20 5.4 Retirement Funds**1 of 30**“Jack - Cigarettes” Big mistake. I waited until I was 30 to quit. A pack now costs $6. I’ll save the way Jill did. Deposit the money daily in an account paying 8% interest. • $205,729 • $274,305 • $482,976 • $643,968 How much will Jack have when he is 60? 5.4 Retirement Funds**1 of 30**How much did Jack and Jill each deposit in their accounts over the years? • Jill deposited more • Jack deposited more • They deposited the same amount 5.4 Retirement Funds**Rule 3**The earlier you begin to invest the better Chart 21 5.4 Retirement Funds**1 of 30**. . 18 years later = ? 4-year tuition now $85,000 3% annual increase • $241 • $506 • $3,174 monthly Goal age 18 + + = ? 10% / year $0 5.4 Retirement Funds**Millionaire (Twice over)**No trick, Oprah. Just takes some time. Hi folks. Our guest promises that she can make your child into a “double-millionaire” painlessly. Must be a catch. Two steps. First, on each of her birthdays from 1 - 21 put $500 in an account earning 10% interest compounded annually. Time we have. Let’s get to the details Second step. Make no more payments. Simply leave the balance in the same account compounded annually until age 65. What could be easier? I hear you, but I have to see the numbers. 23 5.4 Retirement Funds**1 of 30**Invest $500 each year from 1-21 at 10% compounded annually. At age 21 put the balance (nearest dollar) in same account and leave to age 65 making no more payments. Would the child have $2 million at age 65? • No, $1,897,637 • No, $1,927,758 • Yes, $2,120,517 • Yes, $2,446,854 5.4 Retirement Funds**1 of 30**What of these recursion formulas would you use to compute the child’s balance? • Ans + (.10/12)*Answer + 500 • Ans + (10/12)*Answer + 500 • Ans + 10*Answer + 500 • Ans + .10*Answer + 500 5.4 Retirement Funds**1 of 30**Years ago real estate agent Brian Cohee bought a digital camera. Until then he spent $14 developing film for each of the 20 home appraisals he did each week. Now he spends no money for developing.Each Friday Mr. Cohee set aside the money he saved from the 20 appraisals and invested it at 5% interest compounded weekly. He now has $47,101. Assume he works 52 weeks a year. How many years ago did he buy his camera? • A little less than 1 year • About 2.5 years • 3 years • None of the above 5.4 Retirement Funds**End of 5.5**27 5.4 Retirement Funds**Year after**End of year Year after End of Year End of year Year after Start Year after End of year Next year $1,000 $1,000 $1,000 $1,000 10% Interest 10% Interest 10% Interest 10% Interest 10% Interest $5,105 $1,000 $3,641 $3,310 $2,310 $2,100 $1,100 $0 $4,641 28 5.4 Retirement Funds**Start Early Blue: yearly contributionRed: yearly earned**interest After 15 years you earn more interest than you invest After 23 years you earn twice as much as you invest After 29 years you earn three times as much as you invest 5.4 Retirement Funds**Meta-Material**30 5.4 Retirement Funds