5.4 Retirement Funds 1 Section 5.4 Annuities (Retirement Funds) Alaysia

5.4 Retirement Funds 2 I see how investing in a retirement fund is an example of recursion 1.Absolutely 2.Sort of 3.Not a clue Explain:

5.4 Retirement Funds 3 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? 1.$40,000 2.$80,015 3.$120,565 4.$442,593

5.4 Retirement Funds 4 What is the total amount that Alaysia will deposit in her account until she retires? 1.$40,000 2.$60,000 3.$80,000

5.4 Retirement Funds 5 Which recursion formula calculates Alaysia’s balance? 1.Ans+.10*Ans Ans+.10*Ans Ans-.10*Ans Ans-.10*Ans+1000

5.4 Retirement Funds 66 Age 25 $0 Age 26$1,000 Age 27 In general, “Alaysia” $1000/year 10%

5.4 Retirement Funds 7 How much Alaysia will have if she takes an early retirement at 55? (Ans) 10% ++= + $1,000Age 55$0 Age 25 ? 1. $40,000 2.$80,015 3.$120,565 4.$442,593

5.4 Retirement Funds 8 “Alaysia” $ Years $ Which graph best describes the growth of Alaysia’s retirement fund? Years $ $

5.4 Retirement Funds 9 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* How many errors did you make? or more

5.4 Retirement Funds 10 Annuities (APPS) N Number of payments made – years I%Annual interest rate – %, not a decimal PV 0 PMT Your periodic payment – as a negative (-) FVValue of the account after N payments P/Y Number of payments per year C/Y Number of compoundings per year

5.4 Retirement Funds 11 Using APPS verify that Alaysia will have $442,493 10% ++= $1,000Age 65$0 ? N = I% = PV = PMT = FV = P/Y = C/Y =

5.4 Retirement Funds 12 Volatility: Stock Market Returns Fluctuate from Year to Year S&P 500 Total Return Source: Bloomberg Stock Market Returns Despite a history of outperforming other types of securities, stocks sometimes lose money. Sometimes these losses can be substantial and last for long periods. The average annual return on stocks from 1926 to 2005 is about 10.4 percent.

5.4 Retirement Funds 13 From , 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.

5.4 Retirement Funds 14 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? 1. $97, $103, $135, $139,233

5.4 Retirement Funds 15 Rule 1 A slightly higher interest rate can earn substantially more money in the long run

5.4 Retirement Funds 16

5.4 Retirement Funds 17 Rule 2 Small payments over time can earn huge amounts of money

5.4 Retirement Funds 18 “Jill - Cigarettes” 8% ++= $4.50 Age 60 $0 age 20 ? $4.50 per pack 1. $1, $48, $482, $4,829,757 Daily

5.4 Retirement Funds 19 “Jack - Cigarettes” 1. $205, $274, $482, $643,968 How much will Jack have when he is 60? 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.

5.4 Retirement Funds 20 How much did Jack and Jill each deposit in their accounts over the years? 1.Jill deposited more 2.Jack deposited more 3.They deposited the same amount

5.4 Retirement Funds 21 Rule 3 The earlier you begin to invest the better Chart

5.4 Retirement Funds $ $ $3,174 ++= Goal age 18 $0 10% / year 4-year tuition now $85,000 3% annual increase 18 years later = ? ?. monthly

5.4 Retirement Funds 23 Millionaire (Twice over) Hi folks. Our guest promises that she can make your child into a “double-millionaire” painlessly. Must be a catch. No trick, Oprah. Just takes some time. Time we have. Let’s get to the details Two steps. First, on each of her birthdays from put $500 in an account earning 10% interest compounded annually. 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.

5.4 Retirement Funds 24 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? 1. No, $1,897, No, $1,927, Yes, $2,120, Yes, $2,446,854

5.4 Retirement Funds 25 What of these recursion formulas would you use to compute the child’s balance? 1.Ans + (.10/12)*Answer Ans + (10/12)*Answer Ans + 10*Answer Ans +.10*Answer + 500

5.4 Retirement Funds 26 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? 1.A little less than 1 year 2.About 2.5 years 3.3 years 4.None of the above

5.4 Retirement Funds 27 End of 5.5

5.4 Retirement Funds 28 $0$1,100$2,100$1,000$2,310$3,310$3,641$4,641$5,105 $1,000 10% Interest

5.4 Retirement Funds 29 compound interest / start early compound interest 40 years at 5% blue: yearly contribution, red: yearly earned interest After 15 years you will earn more interest then you put into the pot yourself. So now your pot grows already at double speed (your deposit plus interest) Another 8 years later you earn double as much in interest than your yearly contributions, you have increased saving speed to factor 3! Now it takes only another 6 years to triple interest earnings, and so on.... compound interest / start early compound interest 40 years at 5% blue: yearly contribution, red: yearly earned interest After 15 years you will earn more interest then you put into the pot yourself. So now your pot grows already at double speed (your deposit plus interest) Another 8 years later you earn double as much in interest than your yearly contributions, you have increased saving speed to factor 3! Now it takes only another 6 years to triple interest earnings, and so on.... Imagine you put away the same amount of money every year, and you achieve an annual return of let's say 7%, reduced by 2% annual inflation. (a 5% real return) Very boring prospect you might think, but:inflation compound interest / start early compound interest 40 years at 5% blue: yearly contribution, red: yearly earned interest After 15 years you will earn more interest then you put into the pot yourself. So now your pot grows already at double speed (your deposit plus interest) Another 8 years later you earn double as much in interest than your yearly contributions, you have increased saving speed to factor 3! Now it takes only another 6 years to triple interest earnings, and so on.... Start Early Blue: yearly contribution Red: yearly earned interest After 29 years you earn three times as much as you invest After 23 years you earn twice as much as you invest After 15 years you earn more interest than you invest

5.4 Retirement Funds 30 Meta-Material