11-2 Terms to be familiar with…

Interest

Interest

• Money charged for the use of money

Principal

Principal

• The amount of money initially invested

Account Balance

Account Balance

• Amount of money in the account at a given time

Interest Rate

Interest Rate

Percent charged annually a.k.a. APR

Compound Interest

Compound Interest

• Interest charged on interest

Number of times interest is usually compounded

Annually Semi-annually

Quarterly Monthly Weekly Daily Continu-ously

Number of times interest is usually compounded

Annually Semi-annually

Quarterly Monthly Weekly Daily Continu-ously

1

Number of times interest is usually compounded

Annually Semi-annually

Quarterly Monthly Weekly Daily Continu-ously

1 2

Number of times interest is usually compounded

Annually Semi-annually

Quarterly Monthly Weekly Daily Continu-ously

1 2 4

Number of times interest is usually compounded

Annually Semi-annually

Quarterly Monthly Weekly Daily Continu-ously

1 2 4 12

Number of times interest is usually compounded

Annually Semi-annually

Quarterly Monthly Weekly Daily Continu-ously

1 2 4 12 52

Number of times interest is usually compounded

Annually Semi-annually

Quarterly Monthly Weekly Daily Continu-ously

1 2 4 12 52 365

Number of times interest is usually compounded

Annually Semi-annually

Quarterly Monthly Weekly Daily Continu-ously

1 2 4 12 52 365 ∞

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) quarterly b) 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 = .09n = 4t = 5

A = 1200(1 + .09/4)(4 5)∙

A = $1872.61

$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 = .09n = 12t = 5

A = 1200(1 + .09/12)(12 5)∙

A = $1878.81

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 = 10,000n = 2t = 18r = .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 = 10,000n = 365t = 18r = .055

A = 10000(1 + .055/365)(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 = 100,000P = ???n = 52t = 30r = .07

100000 = P(1 + .07/52)(52 30)∙

100000 = P (1 + .07/52)(52 30)∙

$12,262.95 = 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 = 20,000P = 10,000n = 4t = 10r = ????

20000 = 10,000(1 + r/4)(4 10)∙

2 = (1 + r/4)(4 10)∙

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

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

4((2)1/40 – 1) = (r/4) 4∙

4((2)1/40 – 1) = r

r = 0.0699 = 6.99%