Compound Interest

1. Section 7-4
Compound Interest

2. Warm-up
Evaluate to the nearest hundredth.
( ) ( )
4 3
1. 5000 1.07 2. 2500 1.0625
( ) ( )
4(5) 12(3)
3. 3000 1 + 4. 10000 1 +
.06 .085
4 12

3. Warm-up
Evaluate to the nearest hundredth.
( ) ( )
4 3
1. 5000 1.07 2. 2500 1.0625
6553.98
( ) ( )
4(5) 12(3)
3. 3000 1 + 4. 10000 1 +
.06 .085
4 12

4. Warm-up
Evaluate to the nearest hundredth.
( ) ( )
4 3
1. 5000 1.07 2. 2500 1.0625
6553.98 2998.66
( ) ( )
4(5) 12(3)
3. 3000 1 + 4. 10000 1 +
.06 .085
4 12

5. Warm-up
Evaluate to the nearest hundredth.
( ) ( )
4 3
1. 5000 1.07 2. 2500 1.0625
6553.98 2998.66
( ) ( )
4(5) 12(3)
3. 3000 1 + 4. 10000 1 +
.06 .085
4 12
4040.57

6. Warm-up
Evaluate to the nearest hundredth.
( ) ( )
4 3
1. 5000 1.07 2. 2500 1.0625
6553.98 2998.66
( ) ( )
4(5) 12(3)
3. 3000 1 + 4. 10000 1 +
.06 .085
4 12
4040.57 12893.02

7. Compounding:

8. Compounding: Earning interest on interest

9. Compounding: Earning interest on interest
Principal:

10. Compounding: Earning interest on interest
Principal: The original/starting amount

11. Compounding: Earning interest on interest
Principal: The original/starting amount
Annual Compound Interest Formula:

12. Compounding: Earning interest on interest
Principal: The original/starting amount
Annual Compound Interest Formula: A = P(1 + r)
t

13. 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

14. Example 1
Fuzzy Jeff invested $4000 in an account with an annual
yield of 6.2% for 4 years. How much interest does he
earn?

15. Example 1
Fuzzy 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

16. Example 1
Fuzzy 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

17. Example 1
Fuzzy 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

18. Example 1
Fuzzy 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

19. Example 1
Fuzzy 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

20. Example 1
Fuzzy 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.

21. Common Ways to Compound
Annually:

22. Common Ways to Compound
Annually: Once per year

23. Common Ways to Compound
Annually: Once per year
Semi-annually:

24. Common Ways to Compound
Annually: Once per year
Semi-annually: Twice per year

25. Common Ways to Compound
Annually: Once per year
Semi-annually: Twice per year
Quarterly:

26. Common Ways to Compound
Annually: Once per year
Semi-annually: Twice per year
Quarterly: Four times per year

27. Common Ways to Compound
Annually: Once per year
Semi-annually: Twice per year
Quarterly: Four times per year
Monthly:

28. Common Ways to Compound
Annually: Once per year
Semi-annually: Twice per year
Quarterly: Four times per year
Monthly: Twelve times per year

29. General Compound Interest
Formula

30. General Compound Interest
Formula
( )
nt
A = P 1+ r
n

31. General Compound Interest
Formula
( )
nt
A = P 1+ r
n
A = final amount, P = principal,
r = interest rate, t = time in years,
n = number of times compounded in a year

32. Example 2
Maggie 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?

33. Example 2
Maggie 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?
( )
nt
A = P 1+ r
n

34. Example 2
Maggie 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?
()
nt
A = P 1+ r
n
A = 3500 (1 + )
4(5)
.053
4

35. Example 2
Maggie 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?
()
nt
A = P 1+ r
n
A = 3500 (1 + )
4(5)
.053
4
A = 4554.08

36. Example 2
Maggie 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?
()
nt
A = P 1+ r
n
A = 3500 (1 + )
4(5)
.053
4
A = 4554.08
Maggie will have $4554.08.

37. Homework

38. 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