Warm-upsWarm-upsYou deposit $1000 in a savings

account that yields 6% simple interest. After two years what is you account balance

The balance for years 0, 1 and 2 are $1000, $1060 and $1120. Is this an arithmetic or geometric series. Explain your answer

Write a closed form expression for the above case given the general closed form equation An = A0 + (n)(d)

7.2 Growth from Money to 7.2 Growth from Money to MooseMooseCompound Interest – When

interest is paid on both the principal and the earned interest.

Compounded Annually – when the interest on a growth of a savings account is calculate once a year.

Multiplicative Model – when the same number gets multiplied repetitively by some initial value.

Geometric Sequence – a sequence of numbers that has the property that the ratio btw 2 successive term is constant.

Growth Factor – The constant ratio. It is represented by the letter b.

Closed form – an = a0( b )n

Recursive Form – An = An-1 * r + An-1 or

7.2 The Times Are A’ 7.2 The Times Are A’ Changin’Changin’Turn to page 402.Complete problems # 1 – 5 skip 4!

For the table in question 1:◦Interest Earned = Beginning

Balance*0.05◦Ending Balance = Beginning Balance +

Interest ◦Beginning Balance for year 1 is the

Ending Balance for year 0!

7.2 The Times Are A’ 7.2 The Times Are A’ Changin’Changin’Annual Interest Model: A = P(b)t

where b = 1 + r and is called the growth factor

A = Account balance in the futureP = principal (initial deposit) r = rate (as a decimal) t = years also written as A = P(1 + r)t

Example: If you deposit $300 in an account that pays 5% interest what will the balance be in 10 years?

P = 300 r = 5% = .05 t = 10Growth factor: b = 1 + r = 1 + .05 = 1.05 A = 300(1.05)10 = $488.67

7.2 The Times Are A’ 7.2 The Times Are A’ Changin’Changin’

Annual Interest Model: A = P(b)t also written as A = P(1 + r)t

Example: If you deposit $1,000 in an account that pays 9% interest what will the balance be in 5 years?

P = 1,000 r = 9% = .09 t = 5Growth factor: b = 1 + r = 1 + .09 = 1.09 A = 1,000(1.09)5 = $1538.62

WorksheetWorksheetComplete the following Millionaire Work sheet

7.2 The Times Are A’ 7.2 The Times Are A’ Changin’Changin’Compounding Period: How many

times interest is applied to the money in your bank per year.

Turn to page 405 and complete question 6.

6 a) interest should be half! b) remember growth factor =

1 + r

7.2 The Times Are A’ 7.2 The Times Are A’ Changin’Changin’#6a) Cut it in half! 6/2 = 3%!b) b = 1 + r = 1 + .03 = 1.03c)

TermTerm Beg. Beg. BalanceBalance

Interest Interest EarnedEarned

Ending Ending BalanceBalance

1rst 1rst 6months6months

$1600$1600 $48$48 $1648$1648

22ndnd 6months6months

$1648$1648 $49.44$49.44 $1697.44$1697.44

7) to find the ratio = current year’s bal

previous year’s bal

1600/1647.44 = 1.0609

7.2 The Times Are A’ 7.2 The Times Are A’ Changin’Changin’

Turn to page 405 and complete question 7

7 a) Ending Balance = Beginning Balance * 1.032

7 b) 1,600*1.032 = $1,697.44 7 c) 1,600*1.0320 = $2,889.787 d) calculator . . . .

Compound Interest Compound Interest EquationEquation

A = P(1 + r/n)nt

P : initial deposit or principal sometimes labeled a0.

r : interest rate in decimal form (5% = .05).n : compounding period. How many times

interest is applied per year (daily, n = 365).t : years.

ExamplesExamples

IF you deposit $100 into and account that pays 7% interest compound quarterly what will the balance be in 20 years?

P = 100 r = 7% = .07n = quarterly = 4 t = 20

A = P(1 + r/n)nt

A = 100(1 + .07/4)(4*20) parenthesis

A = $400.64

ExamplesExamples

IF you deposit $500 into and account that pays 5% interest compound monthly what will the balance be in 10 years?

P = 500 r = 5% = .05n = monthly = 12 t = 10

A = P(1 + r/n)nt

A = 500(1 + .05/12)(12*10)

parenthesis

A = $823.50

ExamplesExamples

IF you deposit $2,000 into and account that pays 2.5% interest compound annually what will the balance be in 5 years?

P = 2,000 r = 2.5% = .025n = annually = 1 t = 5

A = P(1 + r/n)nt

A = 2000(1 + .025/1)(1*5) parenthesis

A = $2,262.82

ExamplesExamples

IF you deposit $50 into and account that pays 6.2% interest compound weekly what will the balance be in 15 years?

P = 50 r = 6.2% = .062n = weekly = 52 t = 15

A = P(1 + r/n)nt

A = 50(1 + .062/52)(52*15)

parenthesis

A = $126.65

ExamplesExamples

How much do you have to deposit into an account that pays 8% interest compounded daily so that in 10 years you have $600?

P = ? A = 600 r = 8% = .08n = daily = 365 t = 10

A = P(1 + r/n)nt

600 = P(1 + .08/365)(365*10)

600 = P*2.225 P = $269.62

ExamplesExamples

IF you deposit $430 into and account that pays 4% interest compound three times a year how long until your account has over $1,000?

P = 430 r = 4% = .04n = three times = 3 t = ?

A = P(1 + r/n)nt

A = 430(1 + .04/3)(3*t) parenthesis

Guess and check

7.2 The Times Are A’ 7.2 The Times Are A’ Changin’Changin’Lets finish this!

Turn to page 408 and complete # 9 – 10.

When you finish you can start page 410 # 1-4

Compound Interest Compound Interest WorksheetWorksheet

Compound Interest Home Compound Interest Home workworkCompound Interest worksheet

Warm - UpWarm - Up You deposit $500 in an account

that pays 2.5% interest every year.

1) What will the balance be in 10 years?

2) How long until the balance doubles?3) What would you have to deposit

initially to have $1,000 in your account after 5 years using the same interest rate?

Warm - UpWarm - Up Suppose you deposit $1,000 in a bank

account that pays 8% interest per year. What will your balance be in 1 year if…..

1) Your interest is applied once a year.2) Your interest is applied twice a year (be

sure to adjust the interest rate).3) Your interest is applied four times a year

(be sure to adjust the interest rate).4) How much more interest do you make

when applying interest 4 times over a year instead of once?