11-2 Terms to be familiar with…

Interest

Money charged for the use of money

Principal

The amount of money initially invested

Account Balance

Amount of money in the account at a given time

Interest Rate

Percent charged annually a.k.a. APR

Compound Interest

Interest charged on interest

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

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

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

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

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

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

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

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

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

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

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

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

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

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)

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

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

$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 =

$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

A = 1200(1 +.09/4) (4∙5)

A = $

$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 =

$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

A = 1200(1 +.09/12) (12∙5)

A = $

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?

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

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

A = 10000(1 +.06/2) (2∙18)

A = $28,982.78

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

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

A = 10000( /365) (365∙18)

A = $26,910.33

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.

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

= P(1 +.07/52) (52∙30)

= P (1 +.07/52) (52∙30)

$12, = P

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?

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

20000 = 10,000(1 + r/4) (4∙10)

2 = (1 + r/4) (4∙10)

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

(2) 1/ = r/4

4((2) 1/40 – 1) = (r/4)∙4

4((2) 1/40 – 1) = r

r = = 6.99%