aa section 7-4

Section 7-4Compound Interest

Warm-upEvaluate to the nearest hundredth.

1. 5000 1.07( )4

2. 2500 1.0625( )3

3. 3000 1+ .06

4( )4(5)

4. 10000 1+ .085

12( )12(3)

Warm-upEvaluate to the nearest hundredth.

1. 5000 1.07( )4

2. 2500 1.0625( )3

3. 3000 1+ .06

4( )4(5)

4. 10000 1+ .085

12( )12(3)

6553.98

Warm-upEvaluate to the nearest hundredth.

1. 5000 1.07( )4

2. 2500 1.0625( )3

3. 3000 1+ .06

4( )4(5)

4. 10000 1+ .085

12( )12(3)

6553.98 2998.66

Warm-upEvaluate to the nearest hundredth.

1. 5000 1.07( )4

2. 2500 1.0625( )3

3. 3000 1+ .06

4( )4(5)

4. 10000 1+ .085

12( )12(3)

6553.98 2998.66

4040.57

Warm-upEvaluate to the nearest hundredth.

1. 5000 1.07( )4

2. 2500 1.0625( )3

3. 3000 1+ .06

4( )4(5)

4. 10000 1+ .085

12( )12(3)

6553.98 2998.66

4040.57 12893.02

Compounding:

Compounding: Earning interest on interest

Compounding: Earning interest on interest

Principal:

Compounding: Earning interest on interest

Principal: The original/starting amount

Compounding: Earning interest on interest

Principal: The original/starting amount

Annual Compound Interest Formula:

Compounding: Earning interest on interest

Principal: The original/starting amount

Annual Compound Interest Formula: A = P(1+ r)t

Compounding: Earning interest on interest

Principal: The original/starting amount

Annual Compound Interest Formula: A = P(1+ r)t

A = final amount, P = principal, r = interest rate,t = time in years

Example 1Fuzzy Jeff invested $4000 in an account with an annual

yield of 6.2% for 4 years. How much interest does he earn?

Example 1Fuzzy Jeff invested $4000 in an account with an annual

yield of 6.2% for 4 years. How much interest does he earn?

A = P(1+ r)t

Example 1Fuzzy Jeff invested $4000 in an account with an annual

yield of 6.2% for 4 years. How much interest does he earn?

A = P(1+ r)t

A = 4000(1+ .062)4

Example 1Fuzzy Jeff invested $4000 in an account with an annual

yield of 6.2% for 4 years. How much interest does he earn?

A = P(1+ r)t

A = 4000(1+ .062)4

A ≈ 5088.13

Example 1Fuzzy Jeff invested $4000 in an account with an annual

yield of 6.2% for 4 years. How much interest does he earn?

A = P(1+ r)t

A = 4000(1+ .062)4

A ≈ 5088.13

5088.13 − 4000

Example 1Fuzzy Jeff invested $4000 in an account with an annual

yield of 6.2% for 4 years. How much interest does he earn?

A = P(1+ r)t

A = 4000(1+ .062)4

A ≈ 5088.13

5088.13 − 4000 = 1088.13

Example 1Fuzzy Jeff invested $4000 in an account with an annual

yield of 6.2% for 4 years. How much interest does he earn?

A = P(1+ r)t

A = 4000(1+ .062)4

A ≈ 5088.13

5088.13 − 4000 = 1088.13

Jeff earns $1088.13 in interest.

Common Ways to Compound

Annually:

Common Ways to Compound

Annually: Once per year

Common Ways to Compound

Annually: Once per year

Semi-annually:

Common Ways to Compound

Annually: Once per year

Semi-annually: Twice per year

Common Ways to Compound

Annually: Once per year

Semi-annually: Twice per year

Quarterly:

Common Ways to Compound

Annually: Once per year

Semi-annually: Twice per year

Quarterly: Four times per year

Common Ways to Compound

Annually: Once per year

Semi-annually: Twice per year

Quarterly: Four times per year

Monthly:

Common Ways to Compound

Annually: Once per year

Semi-annually: Twice per year

Quarterly: Four times per year

Monthly: Twelve times per year

General Compound Interest Formula

General Compound Interest Formula

A = P 1+ r

n( )nt

General Compound Interest Formula

A = P 1+ r

n( )nt

A = final amount, P = principal, r = interest rate, t = time in years,

n = number of times compounded in a year

Example 2Maggie Brann invests $3500 at an annual yield of 5.3%, compounded quarterly for 5 years. How much money

will she have if she leaves it all in the bank?

Example 2Maggie Brann invests $3500 at an annual yield of 5.3%, compounded quarterly for 5 years. How much money

will she have if she leaves it all in the bank?

A = P 1+ r

n( )nt

Example 2Maggie Brann invests $3500 at an annual yield of 5.3%, compounded quarterly for 5 years. How much money

will she have if she leaves it all in the bank?

A = P 1+ r

n( )nt

A = 3500 1+ .053

4( )4(5)

Example 2Maggie Brann invests $3500 at an annual yield of 5.3%, compounded quarterly for 5 years. How much money

will she have if she leaves it all in the bank?

A = P 1+ r

n( )nt

A = 3500 1+ .053

4( )4(5)

A = 4554.08

Example 2Maggie Brann invests $3500 at an annual yield of 5.3%, compounded quarterly for 5 years. How much money

will she have if she leaves it all in the bank?

A = P 1+ r

n( )nt

A = 3500 1+ .053

4( )4(5)

A = 4554.08Maggie will have $4554.08.

Homework

Homework

p. 441 #1-25, skip 18

“I’m not going to die because I failed as someone else. I’m going to succeed as myself.” - Margaret Cho