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11-2 Terms to be familiar with…

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Interest

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Money charged for the use of money

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Principal

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The amount of money initially invested

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Account Balance

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Amount of money in the account at a given time

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Interest Rate

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Percent charged annually a.k.a. APR

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Compound Interest

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Interest charged on interest

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Number of times interest is usually compounded AnnuallySemi- annually QuarterlyMonthlyWeeklyDailyContinu- ously

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Number of times interest is usually compounded AnnuallySemi- annually QuarterlyMonthlyWeeklyDailyContinu- ously 1

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Number of times interest is usually compounded AnnuallySemi- annually QuarterlyMonthlyWeeklyDailyContinu- ously 12

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Number of times interest is usually compounded AnnuallySemi- annually QuarterlyMonthlyWeeklyDailyContinu- ously 124

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Number of times interest is usually compounded AnnuallySemi- annually QuarterlyMonthlyWeeklyDailyContinu- ously 12412

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Number of times interest is usually compounded AnnuallySemi- annually QuarterlyMonthlyWeeklyDailyContinu- ously 1241252

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Number of times interest is usually compounded AnnuallySemi- annually QuarterlyMonthlyWeeklyDailyContinu- ously 1241252365

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Number of times interest is usually compounded AnnuallySemi- annually QuarterlyMonthlyWeeklyDailyContinu- ously 1241252365 ∞

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Compounded Interest Formula A = P = n = t = r =

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Compounded Interest Formula A = Account Balance P = n = t = r =

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Compounded Interest Formula A = Account Balance P = Principal n = t = r =

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Compounded Interest Formula A = Account Balance P = Principal n = number of times in year interest is compounded t = r =

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Compounded Interest Formula A = Account Balance P = Principal n = number of times in year interest is compounded t = time in years r =

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Compounded Interest Formula A = Account Balance P = Principal n = number of times in year interest is compounded t = time in years r = annual percentage rate (as a decimal)

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Compounded Interest Formula A = P(1 + r/n ) (nt)

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Example1 $1200 is invested at an APR of 9%. Find the balance in five years if the interest is compounded a)quarterlyb) monthly

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$1200 is invested at an APR of 9%. Find the balance in five years if the interest is compounded a)quarterly A = P = r = n = t =

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$1200 is invested at an APR of 9%. Find the balance in five years if the interest is compounded a)quarterly A = ??? P = 1200 r =.09 n = 4 t = 5

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A = 1200(1 +.09/4) (4∙5)

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A = $1872.61

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$1200 is invested at an APR of 9%. Find the balance in five years if the interest is compounded b)monthly A = P = r = n = t =

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$1200 is invested at an APR of 9%. Find the balance in five years if the interest is compounded b)monthly A = ???? P = 1200 r =.09 n = 12 t = 5

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A = 1200(1 +.09/12) (12∙5)

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A = $1878.81

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Example2 I would like to create a trust fund for my daughter that she can have in 18 years for college. I have $10,000 to invest. Which account would have a greater balance, one earning an APR of 6% compounded semiannually or one that earns an APR of 5.5% compounded daily?

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6% compounded semiannually A = P = n = t = r =

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6% compounded semiannually A = ??? P = 10,000 n = 2 t = 18 r =.06

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A = 10000(1 +.06/2) (2∙18)

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A = $28,982.78

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5.5% compounded daily A = P = n = t = r =

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5.5% compounded daily A = ??? P = 10,000 n = 365 t = 18 r =.055

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A = 10000(1 +.055/365) (365∙18)

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A = $26,910.33

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Example 3 I would like to retire with a balance of $100,000 in an annuity. Find the amount of money to invest initially (principal) if I want to retire in 30 years and I can invest at an APR of 7% compounded weekly.

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7% compounded weekly A = 100,000 P = ??? n = 52 t = 30 r =.07

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100000 = P(1 +.07/52) (52∙30)

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100000 = P (1 +.07/52) (52∙30)

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$12,262.95 = P

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Example 4 At what interest rate do I need to invest $10,000 to double its value in 10 years if interest is compounded quarterly?

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A = 20,000 P = 10,000 n = 4 t = 10 r = ????

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20000 = 10,000(1 + r/4) (4∙10)

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2 = (1 + r/4) (4∙10)

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(2) 1/40 = ((1 + r/4) (40) ) 1/40

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(2) 1/40 - 1 = r/4

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4((2) 1/40 – 1) = (r/4)∙4

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4((2) 1/40 – 1) = r

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r = 0.0699 = 6.99%

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