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

5.2 Compound Interest

1

Recursion

Chapter 5

Examples / “Snowball” /Definition


2

Section 5.2

Compound Interest

Aunt Tilly /Recursion Machine


3

I see how compound interest is an example of recursion

1. Absolutely

2. Sort of

3. Not a clue

Explain:


4

Take an educated guess

Roughly how much will you have in 10 years?

1. $185,000

2. $200,000

3. $236,000

4. $260,000

5. $385,000


5

Definitions

• Interest Rate is

• Interest is

• Your account is Compounded Annually meaning

• Your Balance is


6

Calculate balance by hand

• Start

• 1 year later

• 2 years later

• 3 years later

In general,

Current Balance =

Balance last year .

Yugo


7

Here are the values we have:

Jan 1 2008

$100000

Jan 1 2009

$110000

Jan 1 2010

$121000

Jan 1 2011

$133100

Homescreen on the TI “Ans”

TI


8

Start with $100,000 at 10% interest. How much will you have at the end of 10 years? (nearest answer)

1. $185,000

2. $200,000

3. $236,000

4. $260,000

5. $385,000


9

Which graph best describes the growth of your balance?

$

Years

$

Years

$

Years

$

Years

1.

2.

3.

4.

1. 1

2. 2

3. 3

4. 4

Pots of Gold / Joke


10

With compound interest, the amount of interest you earn each year

Sta

ys th

e sa

me

Incr

ease

s by

the

sa..

Incr

ease

s by

larg

er ..

.

50%

0%

50%

1. Stays the same

2. Increases by the same amount

3. Increases by larger and larger amounts


11

Bad news: Hearing of Tilly’s sudden demise, her husband, Uncle Fester, unexpectedly passed on

Good news:

Annual COMPOUND interest

12%

$200,000 No

w

Another sad story - Quiet please

15 years later

?

http://images.google.com/imgres?imgurl=http://www.alyssaravenwood.com/Images/makeup/old-man-prosthetic.jpg&imgrefurl=http://www.make-upboard.com/showthread.php%3Fp%3D5372&h=800&w=638&sz=224&hl=en&start=30&tbnid=9clzjbop-nzFEM:&tbnh=143&tbnw=114&prev=/images%3Fq%3Dold%2Bman%26start%3D18%26ndsp%3D18%26svnum%3D10%26hl%3Den%26rls%3DTSHA,TSHA:2005-13,TSHA:en%26sa%3DN

http://images.google.com/imgres?imgurl=http://www.dpf.gov.br/DCS/noticias/2005/Julho/08072005_apreensaoSP.jpg&imgrefurl=http://en.wikinews.org/wiki/Talk:Worker&h=880&w=1066&sz=369&hl=en&start=10&tbnid=4hhFuuHnsmH3JM:&tbnh=124&tbnw=150&prev=/images%3Fq%3D%2524100,000%26ndsp%3D20%26svnum%3D10%26hl%3Den%26sa%3DN

http://msshad.typepad.com/ordinaryms/images/cash.jpg



12

Suppose that after three years your balance is $280,986. Which expression gives your balance for the fourth year?

1. 280986 + 10000

2. 280986 + 12*280986

3. 280986 + .12

4. 280986 + .12*280986


13

Suppose that after three years your balance is $280,986. Which expression gives your interest for the fourth year?

280

986

+ 12

*280

986

280

986

+ .1

2*28

0986

12*

2809

86

.12*

2809

86

1

00

11. 280986 +

12*280986

2. 280986 + .12*280986

3. 12*280986

4. .12*280986


14

Your $200,000 is compounded annually at 12%. How much will you have at the end of 15 years?

$547,357 $835,450 $977,422 $1,094,713 $1,226,079

0

1

00

1

1. $547,357

2. $835,450

3. $977,422

4. $1,094,713

5. $1,226,079


15

More Frequent Compounding


16

Complete the first column (red) of following chartassuming 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


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


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

January1. A

2. B

3. Same


19

Why compounding twice a year is . than compounding annually (by hand)


20

$200,000 is invested at 12% interest compounded twice a year. What is your

balance after 2 years?

1. $224,000

2. $250,880

3. $252,495

4. $275,865



21

Now complete the second column (green)

12% interest


Now $200,000 $200,000

1 year later $224,000 $224,720



4 years later $314,704 $318,770


22

April 1January

1Next year

?July 1 October

1

$200,000January 1

Take things one step further

12% interest




23

$200,000 at 12% compounded quarterly for 1 year = ?

1. $220,763

2. $224,720

3. $225,102

4. $318,770



24

Finally, complete the last column (blue)

12% interest


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


25

Rule 1

The more times your account is

compounded each year the more

you earn


26

$200,000 at 12% compounded quarterly for 15 years. How many times must you press ENTER to get the answer?

1. 152. 303. 454. 605. None of the above


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?

1. 1585

2. 5475

3. 10575

4. More


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


29

Compound Interest Formulas(annual compounding)


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


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 =


32

$200,000 at 12% compounded daily for 15 years = ?

1. $1,199,160

2. $1,200,324

3. $1,205,876

4. $1,209,572

N =

I% =

PV =

PMT = 0

FV =

P/Y = 1

C/Y =


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

http://www.johnabbottphoto.com/corporate_Philip_Purcell_1.htm


34

1965 – 1997: $500 annual compounding at 22%. What would be a reasonable counter-offer?

1. $105,001.00

2. $237,752.32

3. $287,425.48

4. $290,057.82

5. $353,870.55

N =

I% =

PV =

PMT = 0

FV =

P/Y = 1

C/Y =


35

A counter-offer based on daily compounding = ?

1. $105,002.00

2. $454,052.52

3. $564,858.76

4. $569,481.45

5. $569,484.76

6. $709,574.48

N =

I% =

PV =

PMT = 0

FV =

P/Y = 1

C/Y =


36

Daily compounding - how much interest would the Barrons have earned just in the year 1997?

1. $91,234.97

2. $112,432.24

3. $457,052.52

4. $569,484.76

N =

I% =

PV =

PMT = 0

FV =

P/Y = 1

C/Y =


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

http://www.iol.ie/~bugscave/offspring/gates_wife.jpg

http://www.iol.ie/~bugscave/offspring/gates_wife.jpg


38

How much interest did Bill and Melinda earn that day? $40 billion at 5% compounded daily for 1 day

1. $5,479

2. $5,618

3. $547,945

4. $5,479,452

5. $5,618,355

N =

I% =

PV =

PMT = 0

FV =

P/Y = 1

C/Y =


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


40

“Doubling Time”

Start today at $40,000

Salary increases7.18 % annually

Years to double your salary?

$80,000

http://images.google.com/imgres?imgurl=http://msshad.typepad.com/ordinaryms/images/cash.jpg&imgrefurl=http://msshad.typepad.com/ordinaryms/muttinjeff/index.html&h=329&w=500&sz=75&hl=en&start=2&um=1&tbnid=VHg6iNZHz9J0ZM:&tbnh=86&tbnw=130&prev=/images%3Fq%3Dcash%26svnum%3D10%26um%3D1%26hl%3Den%26rls%3DTSHA,TSHA:2005-13,TSHA:en




41

How many years to double your salary?$40,000 at 7.18% annually

1. 10 years

2. 11 years

3. 13 years

4. 14 years

N =

I% =

PV =

PMT = 0

FV =

P/Y = 1

C/Y =


42

“ Gender Inequity”

$30,000

$40,000

Men get 3% increase annually for 5 years

% increase?

http://images.google.com/imgres?imgurl=http://www.scdhec.net/health/region7/images/mens.jpg&imgrefurl=http://www.scdhec.net/health/region7/prostate.htm&h=173&w=175&sz=8&hl=en&start=1&um=1&tbnid=cgw3u_tktugLOM:&tbnh=99&tbnw=100&prev=/images%3Fq%3Dmale%2Bsymbol%26svnum%3D10%26um%3D1%26hl%3Den%26rls%3DTSHA,TSHA:2005-13,TSHA:en

http://images.google.com/imgres?imgurl=http://upload.wikimedia.org/wikipedia/commons/thumb/2/23/Female.svg/210px-Female.svg.png&imgrefurl=http://commons.wikimedia.org/wiki/Image:Female.svg&h=210&w=210&sz=7&hl=en&start=19&um=1&tbnid=gCw-ZzeaJias9M:&tbnh=106&tbnw=106&prev=/images%3Fq%3Dfemale%2Bsymbol%26start%3D18%26ndsp%3D18%26svnum%3D10%26um%3D1%26hl%3Den%26rls%3DTSHA,TSHA:2005-13,TSHA:en%26sa%3DN


43

Men at $40K, Women at $30K. Over 5 years men get 3% increases. What % must women get to catch up?

1. 5.2%

2. 5.9%

3. 6.7%

4. 9.1%

5. 10.6%

N =

I% =

PV =

PMT = 0

FV =

P/Y = 1

C/Y =


44

“Good Old Days”

Today’s (2008)tuition

$26,942

1955Tuition

?5%

increase annually

http://images.google.com/imgres?imgurl=http://www.baseball-almanac.com/images/university_of_hartford.jpg&imgrefurl=http://www.baseball-almanac.com/college/university_of_hartford_baseball_players.shtml&h=126&w=126&sz=6&hl=en&start=17&um=1&tbnid=xSWWZM6ghD4a3M:&tbnh=90&tbnw=90&prev=/images%3Fq%3DUniversity%2Bof%2Bhartford%2Blogo%26svnum%3D10%26um%3D1%26hl%3Den%26rls%3DTSHA,TSHA:2005-13,TSHA:en%26sa%3DX


45

What was tuition in 1955? (Tuition today = $26,942, increased 3%

annually)

1. $2,030

2. $3,145

3. $5,995

4. $7,455

N =

I% =

PV =

PMT = 0

FV =

P/Y = 1

C/Y =


46

End of 5.3


47Recursion

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

http://www.cartoonstock.com/lowres/jmo0745l.jpg


48

Snowball


49

Recursion? Recursion? What

the heck is recursion?

Ah! Here it is?

re·cur·sion [ ri kúrzh'n ] noun

Early 17th c. < Latin> "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

http://encarta.msn.com/encnet/features/dictionary/Pronounce.aspx?search=recursion



http://images.google.com/imgres?imgurl=http://www1.istockphoto.com/file_thumbview_approve/138068/2/istockphoto_138068_activities_young_boy_reading.jpg&imgrefurl=http://www.istockphoto.com/imageindex/138/0/138068/Activities_Young_boy_reading.html&h=380&w=285&sz=27&hl=en&start=4&tbnid=KKxtCDKgVFkgXM:&tbnh=123&tbnw=92&prev=/images%3Fq%3Ddictionary%2Bboy%26svnum%3D10%26hl%3Den%26rls%3DTSHA,TSHA:2005-13,TSHA:en%26sa%3DN


50

Thank you Thank you Thank you

Her favorite niece/nephew

$100,000

Dear Aunt Tilly

http://images.google.com/imgres?imgurl=http://theinteriorgallery.com/prod_images_blowup/old-woman-waitress1.jpg&imgrefurl=http://item.express.ebay.com/Restaurant-Retail_Display-Furnishings_Bar-Food-Service-Decor_Old-Woman-Waitress-Life-Size-Statue-Hand-Painted-6FT_W0QQitemZ7620054858QQihZ017QQptdnZBarQ20Q26Q20FoodQ20ServiceQ20DecorQQddnZRestaurantQ20Q26Q20RetailQQadnZDisplayQ20Q26Q20FurnishingsQQcmdZExpressItem&h=715&w=540&sz=104&hl=en&start=120&tbnid=PfxRUPsmFT2BtM:&tbnh=140&tbnw=106&prev=/images%3Fq%3Dold%2Bwoman%26start%3D100%26ndsp%3D20%26svnum%3D10%26hl%3Den%26sa%3DN

http://images.google.com/imgres?imgurl=http://www.geocities.com/heyjude2222/alfred_e_neuman_copy.jpg&imgrefurl=http://www.geocities.com/heyjude2222/Laughs.html&h=191&w=154&sz=23&hl=en&start=8&tbnid=0E_fx_YjWCqigM:&tbnh=103&tbnw=83&prev=/images%3Fq%3Dalfred%2Be%2Bneumann%26svnum%3D10%26hl%3Den

http://images.google.com/imgres?imgurl=http://www.angelshope.org/angel.gif&imgrefurl=http://www.angelshope.org/&h=370&w=342&sz=5&hl=en&start=2&um=1&tbnid=1KAthhxROKDe1M:&tbnh=122&tbnw=113&prev=/images%3Fq%3Dangel%26svnum%3D10%26um%3D1%26hl%3Den%26rls%3DTSHA,TSHA:2005-13,TSHA:en

http://images.google.com/imgres?imgurl=http://images.acclaimimages.com/_gallery/_TN/0001-0506-2310-1057_TN.jpg&imgrefurl=http://www.acclaimimages.com/search_terms/wrist.html&h=100&w=75&sz=3&hl=en&start=5&um=1&tbnid=tPlkxaZch13yPM:&tbnh=82&tbnw=62&prev=/images%3Fq%3Darm%2Breaching%2B%26svnum%3D10%26um%3D1%26hl%3Den%26rls%3DTSHA,TSHA:2005-13,TSHA:en



51

$100,000

10% annual COMPOUND

interest



52

$133,100$146,410$121,000

4 years later1 year later2 years later

Now3 years later

Ok compound interest…

Show me what you’ve got!

$100,000

$110,00010%

compound interest

http://images.google.com/imgres?imgurl=http://www.geocities.com/heyjude2222/alfred_e_neuman_copy.jpg&imgrefurl=http://www.geocities.com/heyjude2222/Laughs.html&h=191&w=154&sz=23&hl=en&start=8&tbnid=0E_fx_YjWCqigM:&tbnh=103&tbnw=83&prev=/images%3Fq%3Dalfred%2Be%2Bneumann%26svnum%3D10%26hl%3Den


53

“HOMESCREEN” on the TI

The YUGO of Methods

Gets us there - Barely


54

$259,374

$100,000

$110,000

$121,000

$133,100

$146,410

10 years

10% interest


55

Math Joke (?)

A dictionary definition

Recursion: See Recursion


56

$200,000

Annual

at 12%

$1,094,713

Semi-annual at

12%

$1,148,698

15 years


57

“APPS” on the TI

The “Aston Martin” of Methods

Gets us there - Powerfully and in style


58

Meta – Material

Documents

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