Warm-ups Warm-ups You 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 A n = A 0 + (n)(d)
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Warm-ups You 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.
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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 . . . .