Download presentation

Presentation is loading. Please wait.

Published byMyles Little Modified over 2 years ago

1
Section 5.1: Simple and Compound Interest

2
Simple Interest Simple Interest: Used to calculate interest on loans…often of one year or less. Formula: I = Prt I : interest earned (or owed) P : principal invested (or borrowed) r : annual interest rate t : time in years

3
Example 1 To buy furniture for a new apartment, Jennifer Wall borrowed $5,000 at 6.5% simple interest for 11 months. a. How much interest will she pay? Simple interest: I = Prt I = ?

4
Example 1 To buy furniture for a new apartment, Jennifer Wall borrowed $5,000 at 6.5% simple interest for 11 months. a. How much interest will she pay? Simple interest: I = Prt I = ?P = $5,000 r =.065 t =11/12

5
Example 1 To buy furniture for a new apartment, Jennifer Wall borrowed $5,000 at 6.5% simple interest for 11 months. a. How much interest will she pay? Simple interest: I = Prt I = ?P = $5,000 r =.065 t =11/12 I = Prt = (5000)(0.065)(11/12) =

6
a. How much interest will she pay? Simple interest: I = Prt I = ?P = $5,000 r =.065 t =11/12 I = Prt = (5000)(0.065)(11/12) = $______

7
Example 1 To buy furniture for a new apartment, Jennifer Wall borrowed $5,000 at 6.5% simple interest for 11 months. a. How much interest will she pay? Simple interest: I = Prt I = ?P = $5,000 r =.065 t =11/12 I = Prt = (5000)(0.065)(11/12) = $297.92

8
Example 1 To buy furniture for a new apartment, Jennifer Wall borrowed $5,000 at 6.5% simple interest for 11 months. b. What is the total amount to be repaid?

9
Example 1 To buy furniture for a new apartment, Jennifer Wall borrowed $5,000 at 6.5% simple interest for 11 months. b. What is the total amount to be repaid? Amount to Repay = Principal + Interest

10
Example 1 To buy furniture for a new apartment, Jennifer Wall borrowed $5,000 at 6.5% simple interest for 11 months. b. What is the total amount to be repaid? Amount to Repay = Principal + Interest = 5000 + 297.92

11
Example 1 To buy furniture for a new apartment, Jennifer Wall borrowed $5,000 at 6.5% simple interest for 11 months. b. What is the total amount to be repaid? Amount to Repay = Principal + Interest = 5000 + 297.92 = $ 5,297.92

12
Example 1 To buy furniture for a new apartment, Jennifer Wall borrowed $5,000 at 6.5% simple interest for 11 months. b. What is the total amount to be repaid? Amount to Repay = Principal + Interest = 5000 + 297.92 = $ 5,297.92 Notice here that we really have: A = P + I … or A = P + Prt = P(1 + rt)

13
Example 1 To buy furniture for a new apartment, Jennifer Wall borrowed $5,000 at 6.5% simple interest for 11 months. b. What is the total amount to be repaid? Amount to Repay = Principal + Interest = 5000 + 297.92 = $ 5,297.92 Notice here that we really have: A = P + I … or A = P + Prt = P(1 + rt) So, if you want a direct formula for A with simple interest, use A = P(1 + rt)

14
Example 1 To buy furniture for a new apartment, Jennifer Wall borrowed $5,000 at 6.5% simple interest for 11 months. b. What is the total amount to be repaid? Amount to Repay = Principal + Interest = 5000 + 297.92 = $ 5,297.92 Notice here that we really have: A = P + I … or A = P + Prt = P(1 + rt) So, if you want a direct formula for A with simple interest, use A = P(1 + rt) and, of course if you only want I, then use I = Prt

15
Alabama will beat Michigan Saturday in Dallas. 1. Yes 2. No

16
Find simple interest $10,502 at 4.2% for 10 months A. $370.66 B. $367.57 C. $404.33 D. $330.81

17
Compound Interest Compound Interest: more commonly used than simple interest. With compound interest, the interest itself earns interest. Formula:

18
Compound Interest Compound Interest: more commonly used than simple interest. With compound interest, the interest itself earns interest. Formula: Where A is the compound amount (includes principal and interest)

19
Compound Interest Compound Interest: more commonly used than simple interest. With compound interest, the interest itself earns interest. Formula: Where A is the compound amount (includes principal and interest) P is the initial investment

20
Compound Interest Compound Interest: more commonly used than simple interest. With compound interest, the interest itself earns interest. Formula: Where A is the compound amount (includes principal and interest) P is the initial investment r is the annual percentage rate

21
Compound Interest Compound Interest: more commonly used than simple interest. With compound interest, the interest itself earns interest. Formula: Where A is the compound amount (includes principal and interest) P is the initial investment r is the annual percentage rate m is the number of compounding periods per year:

22
Compound Interest Compound Interest: more commonly used than simple interest. With compound interest, the interest itself earns interest. Formula: Where A is the compound amount (includes principal and interest) P is the initial investment r is the annual percentage rate m is the number of compounding periods per year: Compounded annually, m = 1 Compounded semiannually, m = 2 Compounded quarterly, m = 4, etc.

23
Compound Interest Compound Interest: more commonly used than simple interest. With compound interest, the interest itself earns interest. Formula: Where A is the compound amount (includes principal and interest) P is the initial investment r is the annual percentage rate m is the number of compounding periods per year: Compounded annually, m = 1 Compounded semiannually, m = 2 Compounded quarterly, m = 4, etc. t is the number of years

24
Compound Interest Compound Interest: more commonly used than simple interest. With compound interest, the interest itself earns interest. Formula: Where A is the compound amount (includes principal and interest) P is the initial investment r is the annual percentage rate m is the number of compounding periods per year: Compounded annually, m = 1 Compounded semiannually, m = 2 Compounded quarterly, m = 4, etc. t is the number of years n = mt is the total # of compounding periods over all t years i = r/m is the interest rate per compounding period

25
Example 2 Suppose that $22,000 is invested at 5.5% interest. Find the amount of money in the account after 5 years if the interest is compounded annually.

26
Example 2 Suppose that $22,000 is invested at 5.5% interest. Find the amount of money in the account after 5 years if the interest is compounded annually.

27
Example 2 Suppose that $22,000 is invested at 5.5% interest. Find the amount of money in the account after 5 years if the interest is compounded annually. A = ?; P = 22,000; r = 0.055; m = 1; t = 5

28
Example 2 Suppose that $22,000 is invested at 5.5% interest. Find the amount of money in the account after 5 years if the interest is compounded annually. A = ?; P = 22,000; r = 0.055; m = 1; t = 5

29
Example 2 Suppose that $22,000 is invested at 5.5% interest. Find the amount of money in the account after 5 years if the interest is compounded annually. A = ?; P = 22,000; r = 0.055; m = 1; t = 5

30
Example 2 Suppose that $22,000 is invested at 5.5% interest. Find the amount of money in the account after 5 years if the interest is compounded annually. A = ?; P = 22,000; r = 0.055; m = 1; t = 5 Find the amount of interest earned.

31
Example 2 Suppose that $22,000 is invested at 5.5% interest. Find the amount of money in the account after 5 years if the interest is compounded annually. A = ?; P = 22,000; r = 0.055; m = 1; t = 5 Find the amount of interest earned. Compound Amount (A) = Principal (P) + Interest (I), so I = A – P

32
Example 2 Suppose that $22,000 is invested at 5.5% interest. Find the amount of money in the account after 5 years if the interest is compounded annually. A = ?; P = 22,000; r = 0.055; m = 1; t = 5 Find the amount of interest earned. Compound Amount (A) = Principal (P) + Interest (I), so I = A – P = 28,753.12 – 22,000 = $ 6,753.12

33
Example 3 If $22,000 is invested at 5.5% interest. Find the amount of money in the account after 5 years if interest is compounded monthly. (Round answer to nearest dollar.)

34
Example 3 If $22,000 is invested at 5.5% interest. Find the amount of money in the account after 5 years if interest is compounded monthly. (Round answer to nearest dollar.)

35
Example 3 If $22,000 is invested at 5.5% interest. Find the amount of money in the account after 5 years if interest is compounded monthly. (Round answer to nearest dollar.) A = ?; P = 22,000; r = 0.055; m = 12; t = 5

36
Example 3 If $22,000 is invested at 5.5% interest. Find the amount of money in the account after 5 years if interest is compounded monthly. (Round answer to nearest dollar.) A = ?; P = 22,000; r = 0.055; m = 12; t = 5

37
Example 3 If $22,000 is invested at 5.5% interest. Find the amount of money in the account after 5 years if interest is compounded monthly. (Round answer to nearest dollar.) A = ?; P = 22,000; r = 0.055; m = 12; t = 5 to the nearest DOLLAR

38
Example 3 If $22,000 is invested at 5.5% interest. Find the amount of money in the account after 5 years if interest is compounded monthly. (Round answer to nearest dollar.) A = ?; P = 22,000; r = 0.055; m = 12; t = 5 to the nearest DOLLAR Find the amount of interest earned.

39
Example 3 If $22,000 is invested at 5.5% interest. Find the amount of money in the account after 5 years if interest is compounded monthly. (Round answer to nearest dollar.) A = ?; P = 22,000; r = 0.055; m = 12; t = 5 to the nearest DOLLAR Find the amount of interest earned. Compound Amount (A) = Principal (P) + Interest (I), so I = A – P

40
Example 3 If $22,000 is invested at 5.5% interest. Find the amount of money in the account after 5 years if interest is compounded monthly. (Round answer to nearest dollar.) A = ?; P = 22,000; r = 0.055; m = 12; t = 5 to the nearest DOLLAR Find the amount of interest earned. Compound Amount (A) = Principal (P) + Interest (I), so I = A – P = 28,945 – 22,000 = $ 6,945

41
Find the compound amount A. $10,444.87 B. $10,433.47 C. $10,350.00 D. $9,695.56 $9000 At 3% compounded semiannually for 5 years

42
Example 4: Effective Rate The Effective Annual Rate (EAR) is the rate that would be paid using simple interest in order to be equivalent to a stated compounded rate.

43
Example 4: Effective Rate The Effective Annual Rate (EAR) is the rate that would be paid using simple interest in order to be equivalent to a stated compounded rate. Financial institutions are usually required by law to provide the effective rate so that consumers can easily compare ‘apples to apples’.

44
Example 4: Effective Rate Ex. Find the effective annual rate corresponding to a rate of 8% compounded quarterly. The Effective Annual Rate (EAR) is the rate that would be paid using simple interest in order to be equivalent to a stated compounded rate. Financial institutions are usually required by law to provide the effective rate so that consumers can easily compare ‘apples to apples’.

45
Example 4: Effective Rate Ex. Find the effective annual rate corresponding to a rate of 8% compounded quarterly. The Effective Annual Rate (EAR) is the rate that would be paid using simple interest in order to be equivalent to a stated compounded rate. Financial institutions are usually required by law to provide the effective rate so that consumers can easily compare ‘apples to apples’. This question is easy to answer if we notice a simplifying fact: The interest rate doesn’t change based on the principal or the amount of time.

46
Example 4: Effective Rate Ex. Find the effective annual rate corresponding to a rate of 8% compounded quarterly. The Effective Annual Rate (EAR) is the rate that would be paid using simple interest in order to be equivalent to a stated compounded rate. Financial institutions are usually required by law to provide the effective rate so that consumers can easily compare ‘apples to apples’. This question is easy to answer if we notice a simplifying fact: The interest rate doesn’t change based on the principal or the amount of time. So, in our formulas, we can just calculate using $1 for 1 year.

47
Example 4: Effective Rate Ex. Find the effective annual rate corresponding to a rate of 8% compounded quarterly. The Effective Annual Rate (EAR) is the rate that would be paid using simple interest in order to be equivalent to a stated compounded rate. Financial institutions are usually required by law to provide the effective rate so that consumers can easily compare ‘apples to apples’. This question is easy to answer if we notice a simplifying fact: The interest rate doesn’t change based on the principal or the amount of time. So, in our formulas, we can just calculate using $1 for 1 year. First see how much would be earned with compounding:

48
Example 4: Effective Rate Ex. Find the effective annual rate corresponding to a rate of 8% compounded quarterly. The Effective Annual Rate (EAR) is the rate that would be paid using simple interest in order to be equivalent to a stated compounded rate. Financial institutions are usually required by law to provide the effective rate so that consumers can easily compare ‘apples to apples’. This question is easy to answer if we notice a simplifying fact: The interest rate doesn’t change based on the principal or the amount of time. So, in our formulas, we can just calculate using $1 for 1 year. First see how much would be earned with compounding:

49
Example 4: Effective Rate Ex. Find the effective annual rate corresponding to a rate of 8% compounded quarterly. The Effective Annual Rate (EAR) is the rate that would be paid using simple interest in order to be equivalent to a stated compounded rate. Financial institutions are usually required by law to provide the effective rate so that consumers can easily compare ‘apples to apples’. This question is easy to answer if we notice a simplifying fact: The interest rate doesn’t change based on the principal or the amount of time. So, in our formulas, we can just calculate using $1 for 1 year. First see how much would be earned with compounding:

50
Example 4: Effective Rate Ex. Find the effective annual rate corresponding to a rate of 8% compounded quarterly. The Effective Annual Rate (EAR) is the rate that would be paid using simple interest in order to be equivalent to a stated compounded rate. Financial institutions are usually required by law to provide the effective rate so that consumers can easily compare ‘apples to apples’. This question is easy to answer if we notice a simplifying fact: The interest rate doesn’t change based on the principal or the amount of time. So, in our formulas, we can just calculate using $1 for 1 year. First see how much would be earned with compounding: So $1 would turn into $1.0824 in 1 year.

51
Example 4: Effective Rate Ex. Find the effective annual rate corresponding to a rate of 8% compounded quarterly. The Effective Annual Rate (EAR) is the rate that would be paid using simple interest in order to be equivalent to a stated compounded rate. Financial institutions are usually required by law to provide the effective rate so that consumers can easily compare ‘apples to apples’. This question is easy to answer if we notice a simplifying fact: The interest rate doesn’t change based on the principal or the amount of time. So, in our formulas, we can just calculate using $1 for 1 year. First see how much would be earned with compounding: So $1 would turn into $1.0824 in 1 year. Now use A = $1.0824 in the simple interest formula & solve for r. (This will be the EAR.)

52
Example 4: Effective Rate Ex. Find the effective annual rate corresponding to a rate of 8% compounded quarterly. The Effective Annual Rate (EAR) is the rate that would be paid using simple interest in order to be equivalent to a stated compounded rate. Financial institutions are usually required by law to provide the effective rate so that consumers can easily compare ‘apples to apples’. This question is easy to answer if we notice a simplifying fact: The interest rate doesn’t change based on the principal or the amount of time. So, in our formulas, we can just calculate using $1 for 1 year. First see how much would be earned with compounding: So $1 would turn into $1.0824 in 1 year. Now use A = $1.0824 in the simple interest formula & solve for r. (This will be the EAR.) A = P(1+rt)

53
Example 4: Effective Rate Ex. Find the effective annual rate corresponding to a rate of 8% compounded quarterly. The Effective Annual Rate (EAR) is the rate that would be paid using simple interest in order to be equivalent to a stated compounded rate. Financial institutions are usually required by law to provide the effective rate so that consumers can easily compare ‘apples to apples’. This question is easy to answer if we notice a simplifying fact: The interest rate doesn’t change based on the principal or the amount of time. So, in our formulas, we can just calculate using $1 for 1 year. First see how much would be earned with compounding: So $1 would turn into $1.0824 in 1 year. Now use A = $1.0824 in the simple interest formula & solve for r. (This will be the EAR.) A = P(1+rt) 1.0824 = 1[1 + r(1)]

54
Example 4: Effective Rate Ex. Find the effective annual rate corresponding to a rate of 8% compounded quarterly. The Effective Annual Rate (EAR) is the rate that would be paid using simple interest in order to be equivalent to a stated compounded rate. Financial institutions are usually required by law to provide the effective rate so that consumers can easily compare ‘apples to apples’. This question is easy to answer if we notice a simplifying fact: The interest rate doesn’t change based on the principal or the amount of time. So, in our formulas, we can just calculate using $1 for 1 year. First see how much would be earned with compounding: So $1 would turn into $1.0824 in 1 year. Now use A = $1.0824 in the simple interest formula & solve for r. (This will be the EAR.) A = P(1+rt) 1.0824 = 1[1 + r(1)] 1.0824 = 1 + r

55
Example 4: Effective Rate Ex. Find the effective annual rate corresponding to a rate of 8% compounded quarterly. The Effective Annual Rate (EAR) is the rate that would be paid using simple interest in order to be equivalent to a stated compounded rate. Financial institutions are usually required by law to provide the effective rate so that consumers can easily compare ‘apples to apples’. This question is easy to answer if we notice a simplifying fact: The interest rate doesn’t change based on the principal or the amount of time. So, in our formulas, we can just calculate using $1 for 1 year. First see how much would be earned with compounding: So $1 would turn into $1.0824 in 1 year. Now use A = $1.0824 in the simple interest formula & solve for r. (This will be the EAR.) A = P(1+rt) 1.0824 = 1[1 + r(1)] 1.0824 = 1 + r r =.0824

56
Example 4: Effective Rate Ex. Find the effective annual rate corresponding to a rate of 8% compounded quarterly. The Effective Annual Rate (EAR) is the rate that would be paid using simple interest in order to be equivalent to a stated compounded rate. Financial institutions are usually required by law to provide the effective rate so that consumers can easily compare ‘apples to apples’. This question is easy to answer if we notice a simplifying fact: The interest rate doesn’t change based on the principal or the amount of time. So, in our formulas, we can just calculate using $1 for 1 year. First see how much would be earned with compounding: So $1 would turn into $1.0824 in 1 year. Now use A = $1.0824 in the simple interest formula & solve for r. (This will be the EAR.) A = P(1+rt) 1.0824 = 1[1 + r(1)] 1.0824 = 1 + r r =.0824 So, the EAR is 8.24%

57
Example 4: Effective Rate If you would rather have a formula for EAR, here it is: The effective rate corresponding to a stated rate of interest r compounded m times per year is This formula gives the same answer that you would get if you just ‘figured it out’ as we did earlier. Try it yourself and see!

58
Example 5 A family plans to retire in 15 years and expects to need $300,000. Determine how much they must invest today at 12.3% compounded semiannually to accomplish their goal.

59
Example 5 A family plans to retire in 15 years and expects to need $300,000. Determine how much they must invest today at 12.3% compounded semiannually to accomplish their goal.

60
Example 5 A family plans to retire in 15 years and expects to need $300,000. Determine how much they must invest today at 12.3% compounded semiannually to accomplish their goal. A = $300,000 P = ? r = 0.123 m = 2 t = 15

61
Example 5 A family plans to retire in 15 years and expects to need $300,000. Determine how much they must invest today at 12.3% compounded semiannually to accomplish their goal. A = $300,000 P = ? r = 0.123 m = 2 t = 15

62
Example 5 A family plans to retire in 15 years and expects to need $300,000. Determine how much they must invest today at 12.3% compounded semiannually to accomplish their goal. A = $300,000 P = ? r = 0.123 m = 2 t = 15 P = $50,063.51

63
How much of this did you understand well today? 1. All or most 2. A lot of it 3. About half of it 4. Not too much of it 5. None or hardly any of it

Similar presentations

Presentation is loading. Please wait....

OK

SECTION 13-1 The Time Value of Money Slide 13-1-1.

SECTION 13-1 The Time Value of Money Slide 13-1-1.

© 2017 SlidePlayer.com Inc.

All rights reserved.

Ads by Google

Ppt on campus recruitment system software Ppt on dna computing in security Ppt on regular expression javascript Ppt on care of public property Ppt on column chromatography uses Ppt on low level languages Ppt on enzymes Ppt on conceptual art history Field emission display ppt on tv Detail ppt on filariasis disease