aa section 7-4
DESCRIPTION
Compound InterestTRANSCRIPT
![Page 1: AA Section 7-4](https://reader035.vdocuments.mx/reader035/viewer/2022062319/5559c8cbd8b42a93208b4641/html5/thumbnails/1.jpg)
Section 7-4Compound Interest
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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)
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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
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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
![Page 5: AA Section 7-4](https://reader035.vdocuments.mx/reader035/viewer/2022062319/5559c8cbd8b42a93208b4641/html5/thumbnails/5.jpg)
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
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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
![Page 7: AA Section 7-4](https://reader035.vdocuments.mx/reader035/viewer/2022062319/5559c8cbd8b42a93208b4641/html5/thumbnails/7.jpg)
Compounding:
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Compounding: Earning interest on interest
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Compounding: Earning interest on interest
Principal:
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Compounding: Earning interest on interest
Principal: The original/starting amount
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Compounding: Earning interest on interest
Principal: The original/starting amount
Annual Compound Interest Formula:
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Compounding: Earning interest on interest
Principal: The original/starting amount
Annual Compound Interest Formula: A = P(1+ r)t
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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
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Example 1Fuzzy Jeff invested $4000 in an account with an annual
yield of 6.2% for 4 years. How much interest does he earn?
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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
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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
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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
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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
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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
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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.
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Common Ways to Compound
Annually:
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Common Ways to Compound
Annually: Once per year
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Common Ways to Compound
Annually: Once per year
Semi-annually:
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Common Ways to Compound
Annually: Once per year
Semi-annually: Twice per year
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Common Ways to Compound
Annually: Once per year
Semi-annually: Twice per year
Quarterly:
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Common Ways to Compound
Annually: Once per year
Semi-annually: Twice per year
Quarterly: Four times per year
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Common Ways to Compound
Annually: Once per year
Semi-annually: Twice per year
Quarterly: Four times per year
Monthly:
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Common Ways to Compound
Annually: Once per year
Semi-annually: Twice per year
Quarterly: Four times per year
Monthly: Twelve times per year
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General Compound Interest Formula
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General Compound Interest Formula
A = P 1+ r
n( )nt
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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
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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?
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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
![Page 34: AA Section 7-4](https://reader035.vdocuments.mx/reader035/viewer/2022062319/5559c8cbd8b42a93208b4641/html5/thumbnails/34.jpg)
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)
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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
![Page 36: AA Section 7-4](https://reader035.vdocuments.mx/reader035/viewer/2022062319/5559c8cbd8b42a93208b4641/html5/thumbnails/36.jpg)
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.
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Homework
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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