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5.2 Compound Interest 1 Recursion Chapter 5 Examples / “Snowball” / Definition

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5.2 Compound Interest 2 Section 5.2 Compound Interest Aunt Tilly / Recursion Machine

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5.2 Compound Interest 3 I see how compound interest is an example of recursion 1.Absolutely 2.Sort of 3.Not a clue Explain:

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5.2 Compound Interest 4 Take an educated guess Roughly how much will you have in 10 years? 1. $185, $200, $236, $260, $385,000

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5.2 Compound Interest 5 Definitions Interest Rate is Interest is Your account is Compounded Annually meaning Your Balance is

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5.2 Compound Interest 6 Calculate balance by hand Start 1 year later 2 years later 3 years later In general, Current Balance = Balance last year. Yugo

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5.2 Compound Interest 7 Here are the values we have: Jan $ Jan $ Jan $ Jan $ Homescreen on the TI “Ans” TI

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5.2 Compound Interest 8 Start with $100,000 at 10% interest. How much will you have at the end of 10 years? (nearest answer) 1. $185, $200, $236, $260, $385,000

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5.2 Compound Interest 9 Which graph best describes the growth of your balance? $ Years $ $ $ Pots of Gold / Joke

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5.2 Compound Interest 10 With compound interest, the amount of interest you earn each year 1.Stays the same 2.Increases by the same amount 3.Increases by larger and larger amounts

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5.2 Compound Interest 11 Bad news: Hearing of Tilly’s sudden demise, her husband, Uncle Fester, unexpectedly passed on Good news: Annual COMPOUND interest 12% $200,000 Now Another sad story - Quiet please 15 years later ?

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5.2 Compound Interest 12 Suppose that after three years your balance is $280,986. Which expression gives your balance for the fourth year? * *280986

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5.2 Compound Interest 13 Suppose that after three years your balance is $280,986. Which expression gives your interest for the fourth year? * * * *280986

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5.2 Compound Interest 14 Your $200,000 is compounded annually at 12%. How much will you have at the end of 15 years? 1. $547, $835, $977, $1,094, $1,226,079

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5.2 Compound Interest 15 More Frequent Compounding

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5.2 Compound Interest 16 Complete the first column (red) of following chart assuming 12% interest Annual Semi-annual Quarterly Now$200,000 1 year later$224,000 2 years later 3 years later 4 years later$314,704

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5.2 Compound Interest 17 Your account at 12 % interest is compounded TWICE a year (July and January). What interest rate will be applied in July? 1. 1% 2. 5% 3. 6% 4. 12% 5. None of the above

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5.2 Compound Interest 18 Which is better? A.Receive 12% interest at the end of the year, or B.Receive % interest in July and another % interest the following January 1. A 2. B 3. Same

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5.2 Compound Interest 19 Why compounding twice a year is. than compounding annually (by hand)

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5.2 Compound Interest 20 $200,000 is invested at 12% interest compounded twice a year. What is your balance after 2 years? 1. $224, $250, $252, $275, None of the above

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5.2 Compound Interest 21 Now complete the second column (green) 12% interest Annual Semi-annual Quarterly Now$200,000 $200,000 1 year later$224,000$224,720 2 years later$250,880 3 years later$280,986 4 years later$314,704$318,770

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5.2 Compound Interest 22 April 1 January 1 Next year ? July 1 October 1 $200,000 January 1 Take things one step further 12% interest

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5.2 Compound Interest 23 $200,000 at 12% compounded quarterly for 1 year = ? 1. $220, $224, $225, $318, None of the above

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5.2 Compound Interest 24 Finally, complete the last column (blue) 12% interest Annual Semi-annual Quarterly Now$200,000 $200,000$200,000 1 year later$224,000$224,720$225,102 2 years later$250,880$252,495 3 years later$280,986$283,704 4 years later$314,704$318,770$320,941

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5.2 Compound Interest 25 Rule 1 The more times your account is compounded each year the more you earn

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5.2 Compound Interest 26 $200,000 at 12% compounded quarterly for 15 years. How many times must you press ENTER to get the answer? None of the above

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5.2 Compound Interest 27 $200,000 at 12% compounded daily for 15 years. ( 365 days per year). How many times must you press ENTER to get the answer? More

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5.2 Compound Interest 28 You invest $1,000 at 12% interest compounded 12 times a year. Which of these recursion formulas would you not use to compute your balance? Aston - Martin 1.Ans + (.12/12)*Ans 2.Ans + (.1)*Ans 3.Ans + (12/12)*Ans 4.(.12/12)*Ans + Ans

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5.2 Compound Interest 29 Compound Interest Formulas (annual compounding)

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5.2 Compound Interest 30 Compound Interest in “APPS” N - The length of the account – in years I% - Annual interest rate as a percent, not a decimal PV - Deposit – negative number FV - Balance after N years C/Y - Times the account is compounded each year ALWAYS Set PMT = 0 – There are no payments Set P/Y = 1 Set the last line to END

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5.2 Compound Interest 31 Using “Ans” on HOMECREEN we saw that $200,000 at 12% compounded annually grew to $1,094,713 after 15 years - Verify this using “APPS” N = I% = PV = PMT = 0 FV = P/Y = 1 C/Y =

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5.2 Compound Interest 32 $200,000 at 12% compounded daily for 15 years = ? 1. $1,199, $1,200, $1,205, $1,209,572 N = I% = PV = PMT = 0 FV = P/Y = 1 C/Y =

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5.2 Compound Interest 33 “Maurice M. Barron” (March 8, 1997) I’m Peter Lynch with Fidelity. You’re right. Tell you what we’ll do. How about $105,000 to settle the matter? Hey Fidelity. What happened to my father’s money? In 1965 he invested $500 with you guys. It’s now 1997 and we haven’t heard a peep Just a minute. I took M116 at UH and remember some of this finance stuff. I’ll get back to you

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5.2 Compound Interest – 1997: $500 annual compounding at 22%. What would be a reasonable counter-offer? 1. $105, $237, $287, $290, $353, N = I% = PV = PMT = 0 FV = P/Y = 1 C/Y =

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5.2 Compound Interest 35 A counter-offer based on daily compounding = ? 1. $105, $454, $564, $569, $569, $709, N = I% = PV = PMT = 0 FV = P/Y = 1 C/Y =

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5.2 Compound Interest 36 Daily compounding - how much interest would the Barrons have earned just in the year 1997? 1. $91, $112, $457, $569, N = I% = PV = PMT = 0 FV = P/Y = 1 C/Y =

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5.2 Compound Interest 37 “Bill and Melinda Gates” Hi Melinda. Tough day at the office? Not so bad. First thing this morning I took our $40 billion and invested it at 5% interest compounded daily. On the way home I withdrew the interest we made today Enough for dinner and a movie? Should cover it

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5.2 Compound Interest 38 How much interest did Bill and Melinda earn that day? $40 billion at 5% compounded daily for 1 day 1. $5, $5, $547, $5,479, $5,618,355 N = I% = PV = PMT = 0 FV = P/Y = 1 C/Y =

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5.2 Compound Interest 39 What of these recursion formulas would you use to compute the Gates’ balance? 1.Ans + (.05/12)*Answer 2.Ans + (5/12)*Answer 3.Ans + (.05/365)*Answer 4.Ans + (0.5/365)*Answer 5.Ans + (5/365)*Answer

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5.2 Compound Interest 40 “Doubling Time” Start today at $40,000 Salary increases 7.18 % annually Years to double your salary? $80,000

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5.2 Compound Interest 41 How many years to double your salary? $40,000 at 7.18% annually years years years years N = I% = PV = PMT = 0 FV = P/Y = 1 C/Y =

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5.2 Compound Interest 42 “ Gender Inequity” $30,000 $40,000 Men get 3% increase annually for 5 years % increase?

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5.2 Compound Interest 43 Men at $40K, Women at $30K. Over 5 years men get 3% increases. What % must women get to catch up? % % % % % N = I% = PV = PMT = 0 FV = P/Y = 1 C/Y =

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5.2 Compound Interest 44 “Good Old Days” Today’s (2008) tuition $26, Tuition ? 5% increase annually

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5.2 Compound Interest 45 What was tuition in 1955? (Tuition today = $26,942, increased 3% annually) 1. $2, $3, $5, $7,455 N = I% = PV = PMT = 0 FV = P/Y = 1 C/Y =

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5.2 Compound Interest 46 End of 5.3

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5.2 Compound Interest 47 Recursion We can give you 12% interest if you never withdraw it I can’t take early retirement. I haven’t paid off my student loan yet ! If you miss a payment we show up and embarrass you in front of your friends

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5.2 Compound Interest 48 Snowball

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5.2 Compound Interest 49 Recursion? Recursion? What the heck is recursion? Ah! Here it is? re·cur·sion [ ri kúrzh'n ] noun ri kúrzh'n Early 17th c. "a running back" 1. The return to something repeatedly 2. Mathematics: the use of repeated steps, each based on the result of the one before to calculate a number

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5.2 Compound Interest 50 Thank you Thank you Thank you Her favorite niece/nephew $100,000 Dear Aunt Tilly

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5.2 Compound Interest 51 $100,000 10% annual COMPOUND interest

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5.2 Compound Interest 52 $133,100 $146,410 $121,000 4 years later1 year later 2 years later Now 3 years later Ok compound interest… Show me what you’ve got! $100,000 $110,000 10% compound interest

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5.2 Compound Interest 53 “HOMESCREEN” on the TI The YUGO of Methods Gets us there - Barely

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5.2 Compound Interest 54 $259,374 $100,000 $110,000 $121,000 $133,100 $146, years 10% interest

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5.2 Compound Interest 55 Math Joke (?) A dictionary definition Recursion: See Recursion

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5.2 Compound Interest 56 $200,000 Annual at 12% Semi-annual $1,094,713 Semi-annual at 12% $1,148,698 Semi-annual 15 years

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5.2 Compound Interest 57 “APPS” on the TI The “Aston Martin” of Methods Gets us there - Powerfully and in style

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5.2 Compound Interest 58 Meta – Material

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