1. Simple Interest and Simple Discount
CHAPTER 11
Simple Interest and Simple Discount

2. Find simple interest by using the simple interest formula.
11-1
Learning Outcomes
Find simple interest by using the simple interest formula.
Find the maturity of a loan.
Convert months to a fractional or decimal part of a year.
Find the principal, rate or time using the simple interest formula.

3. Find simple interest using the simple interest formula
11-1-1
Section 11-1
The Simple Interest Formula
The interest formula shows how interest, rate, and time are related.
It gives us a way of finding one of these values if the other three values are known.
I = P x R x T

4. The price paid for using money is called interest.
HOW TO:
Identify the principal, rate and time
Section 11-1
The Simple Interest Formula
The price paid for using money is called interest.
Principal is the amount borrowed or invested.
Rate is the percent of the principal paid as interest per period, usually one year.
Time must be expressed in the same unit of time as the rate. (i.e. one year)

5. Interest Simple interest Principal Key Terms…
Section 11-1
The Simple Interest Formula
Interest
An amount paid or earned for the use of money.
Simple interest
Interest earned when a loan or investment is repaid in a lump sum.
Principal
The amount of money borrowed or invested.

6. Key Terms…
Section 11-1
The Simple Interest Formula
Rate
The percent of the principal paid as interest per time period.
Time
The number of days, months or years that the money is borrowed or invested.

7. HOW TO:
Find the interest paid on a loan
Section 11-1
The Simple Interest Formula
Principal = (P) = $1,200 Interest rate = 8% (or 0.08) Time = 1 year Interest = P x R x T Interest = 1,200 x 0.08 x 1 Interest = $96 The interest on the loan is $96

8. Find the interest on a 2-year loan of $4,000 at a 6% rate.
Examples…
Section 11-1
The Simple Interest Formula
Find the interest on a 2-year loan of $4,000 at a 6% rate.
$480
Find the interest earned on a 3-year investment of $5,000 at 4.5% interest.
$675

9. If principal and interest are known, add them.
11-1-2
Find the maturity value of a loan
Section 11-1
The Simple Interest Formula
Maturity value is the total amount of money due by the end of a loan period.
The amount of the loan and interest.
If principal and interest are known, add them.
MV = principal + PRT
MV = P(1+RT)

10. What is the maturity value for a $2,500 loan?
An Example…
Section 11-1
The Simple Interest Formula
Marcus Logan can purchase furniture on a 2-year simple interest loan at 9% interest per year.
What is the maturity value for a $2,500 loan?
MV = P(1 + RT); (substitute known values)
MV = $2,500 ( x 2)
MV = $2,500 ( )
MV = $2,500 (1.18)
MV = $2,950
Marcus will pay $2,950 at the end of two years.

11. Examples…
Section 11-1
The Simple Interest Formula
Terry Williams is going to borrow $4,000 at 7.5% interest. What is the maturity value of the loan after three years?
$4,900
Jim Sherman will invest $3,000 at 8% for 5 years. What is the maturity value of the investment?
$4,200

12. Write the number of months as the numerator of a fraction.
Convert months to a fractional or decimal part of a year
11-1-3
Section 11-1
The Simple Interest Formula
Write the number of months as the numerator of a fraction.
Write 12 as the denominator of the fraction.
Reduce the fraction to lowest terms if using the fractional equivalent.
Divide the numerator by the denominator to get the decimal equivalent of the fraction.

13. Convert months to a fractional or decimal part of a year 11-1-3
Section 11-1
The Simple Interest Formula
Convert 9 months & 15 months, respectively, to years, expressing both as fractions & decimals.
9 months = ¾ or 0.75 of a year
15 months = 1 ¼ or 1.25 of a year

14. How much interest did he earn?
An Example…
Section 11-1
The Simple Interest Formula
To save money, Stan Wright invested $2,500 for 42 months at 4 ½ % simple interest.
How much interest did he earn?
42 months = = 3.5
I = P x R x T
I = $2,500 x x 3.5
I = $393.75
Stan will earn $

15. Examples…
Section 11-1
The Simple Interest Formula
Akiko is saving a little extra money to pay for her car insurance next year. If she invests $1,000 for 18 months at 4%, how much interest can she earn?
$60
Habib is going to borrow $2,000 for 42 months at 7% . What will be the amount of interest owed?
$490

16. Find the Principal, Rate or Time Using the Simple Interest Formula
11-1-4
Section 11-1
The Simple Interest Formula

17. How much was the principal? Substitute the known values and solve.
Find the principal using the simple interest formula
HOW TO:
Section 11-1
The Simple Interest Formula
Judy paid $108 in interest on a loan that she had for 6 months. The interest rate was 12%.
How much was the principal?
Substitute the known values and solve.
P = $1,800
P =
P =

18. Find the rate using the simple interest formula HOW TO:
Section 11-1
The Simple Interest Formula
Sam wants to borrow $1,500 for 15 months and will have to pay $225 in interest.
What is the rate he is being charged?
Substitute the known values and solve.
R = .12 or 12%
The rate Sam will pay is 12%.
R =
R =

19. Substitute the known values and solve.
Find the time using the simple interest formula
HOW TO:
Section 11-1
The Simple Interest Formula
Shelby borrowed $10,000 at 8% and paid $1,600 in interest.
What was the length of the loan?
Substitute the known values and solve.
Length of the loan was two years.
T =
T =

20. Find the ordinary interest and the exact interest.
11-2
Learning Outcomes
Find the exact time.
Find the due date.
Find the ordinary interest and the exact interest.
Make a partial payment before the maturity date.

21. Ordinary time Exact time Key Terms…
Section 11-2
Ordinary and Exact Interest
Ordinary time
Time that is based on counting 30 days in each month.
Exact time
Time that is based on counting the exact number of days in a time period.

22. The ordinary time from July 12 to September 12 is 60 days.
11-2-1
Find the exact time
Section 11-2
Ordinary and Exact Interest
The ordinary time from July 12 to September 12 is 60 days.
To find the exact time from July 12 to September 12, add the following:
Days in July (31 – 12) = 19
Days in August
Days in September +12
62 days

23. Example: From May 15 to October 15
HOW TO:
Sequential numbers for dates of the year
Section 11-2
Ordinary and Exact Interest
Find the exact time of a loan using the sequential numbers table. (Table 11-1 in the text)
See page 394
If the beginning and due dates of the loan fall within the same year, subtract the beginning date’s sequential number from the due date’s sequential number.
Example: From May 15 to October 15
288 – 135 = 153 days, the exact time

24. Find the exact time from May 15 of Year 1 to March 15 in Year 2.
An Example…
Section 11-2
Ordinary and Exact Interest
Find the exact time from May 15 of Year 1 to March 15 in Year 2.
365 – 135 = 230
= 304 days
The exact time is 304 days.
Note: If Year 2 is a leap year, the exact time is 305 days.

25. Subtract the beginning date’s sequential number from 365.
11-2-2
Find the due date
Section 11-2
Ordinary and Exact Interest
Subtract the beginning date’s sequential number from 365.
Add the due date’s sequential number to the result from the previous step.
If February 29 falls between the two dates, add 1. (Is it a leap year?)

26. A loan made on September 5 is due July 5 of the following year.
An Example…
Section 11-2
Ordinary and Exact Interest
A loan made on September 5 is due July 5 of the following year.
a) ordinary time b) exact time in a non-leap year c) exact time in a leap year
Find:
Ordinary time = 300 days
Exact time (non-leap year) = 303 days
Exact time (leap year) = 304 days

27. An interest rate is normally given as rate per year.
11-2-3
Find the ordinary and exact interest
Section 11-2
Ordinary and Exact Interest
An interest rate is normally given as rate per year.
If the time period of the loan is in days, using the simple interest formula requires that the rate also be expressed as a rate per day.
Ordinary interest: assumes 360 days per year.

28. Ordinary interest Exact interest Banker’s rule Key Terms…
Section 11-2
Ordinary and Exact Interest
Ordinary interest
A rate per day that assumes 360 days per year.
Exact interest
A rate per day that assumes 365 days per year.
Banker’s rule
Calculating interest on a loan based on ordinary interest which yields a slightly higher amount of interest.

29. Ordinary interest rate per day =
HOW TO:
Find the ordinary interest
Section 11-2
Ordinary and Exact Interest
For ordinary interest rate per day, divide the annual interest rate by 360.
Ordinary interest rate per day =
Interest rate per year
360

30. Exact interest rate per day =
HOW TO:
Find the exact interest
Section 11-2
Ordinary and Exact Interest
For exact interest rate per day, divide the annual interest rate by 365.
Exact interest rate per day =
Interest rate per year
365

31. Length of loan (ordinary time) = 60 days
Use ordinary time to find the ordinary interest on a loan
HOW TO:
Section 11-2
Ordinary and Exact Interest
A loan of $500 at 7% annual interest rate. The loan was made on March 15 and due on May 15. (Principal = $500)
I = P x R x T
Length of loan (ordinary time) = 60 days
Rate = (ordinary interest)
Interest =
= $5.83

32. Length of loan (exact time) = 61 days
Use exact time to find the ordinary interest the same loan
HOW TO:
Section 11-2
Ordinary and Exact Interest
A loan of $500 at 7% annual interest rate. The loan was made on March 15 and due on May 15. (Principal = $500)
I = P x R x T
Length of loan (exact time) = 61 days
Rate = (ordinary interest)
Interest =
= $5.93

33. Length of loan (exact time) = 61 days
Use exact time to find the exact interest the same loan
HOW TO:
Section 11-2
Ordinary and Exact Interest
A loan of $500 at 7% annual interest rate. The loan was made on March 15 and due on May 15. (Principal = $500)
I = P x R x T
Length of loan (exact time) = 61 days
Rate = (ordinary interest)
Interest =
= $5.84

34. STEP 1 STEP 2 Make a Partial Payment Before the Maturity Date 11-2-4
Section 11-2
Ordinary and Exact Interest
To find the adjusted principal and adjusted balance due at maturity for a partial payment made before the maturity date:
Determine the exact time from the date of the loan to the first partial payment.
STEP 1
Calculate the interest using the time found in Step 1.
STEP 2

35. STEP 3 STEP 4 STEP 5 Make a Partial Payment Before the Maturity Date
11-2-4
Section 11-2
Ordinary and Exact Interest
Subtract the amount of interest found in Step 2 from the partial payment.
STEP 3
Subtract the remainder of the partial payment (Step 3) from the original principal. This is the adjusted principal.
STEP 4
Repeat process for additional partial payments.
STEP 5

36. STEP 6 Make a Partial Payment Before the Maturity Date 11-2-4
Section 11-2
Ordinary and Exact Interest
At maturity, calculate interest from the last partial payment and add to adjusted principal. This is the adjusted balance due at maturity.
STEP 6

37. An Example…
Section 11-2
Ordinary and Exact Interest
Tony borrows $5,000 on a 10%, 90 day note. On the 30th day, Tony pays $1,500 on the note. If ordinary interest is applied, what is Tony’s adjusted principal after the partial payment, and adjusted balance due at maturity?
$5,000(0.1)(30 ÷ 360) = $41.67
$1,500 - $41.67 = $1,458.33
$5,000 - $1, = $3, (Adj. Principal)
$3,541.67(.1)(60 ÷ 360) = $59.03 (Interest)
$3, $59.03 = $3, (Adj. Balance)

38. Find the bank discount and proceeds for a simple discount note.
11-3
Learning Outcomes
Find the bank discount and proceeds for a simple discount note.
Find the true effective interest rate of a simple discount note.
Find the third-party discount and proceeds for a third-party discount note.

39. Find the bank discount and proceeds for a simple discount note
11-3-1
Section 11-3
Promissory Notes
For the bank discount, use: Bank discount = face value x disc. rate x time I = P x R x T For the proceeds, use: Proceeds = face value – bank discount A = P - I

40. A Promissory Note
Section 11-3
Promissory Notes

41. To find the true or effective interest rate of a simple discount note:
11-3-2
Section 11-3
Promissory Notes
To find the true or effective interest rate of a simple discount note:
Find the bank discount (interest). I = PRT
STEP 1
STEP 2
Find the proceeds: proceeds = principal – bank discount.
STEP 3
Find the effective interest rate: R = I/PT (using the proceeds as the principal)

42. R or the effective interest rate = 12.4%
An Example…
Section 11-3
Promissory Notes
What is the effective interest rate of a $5,000 simple discount note, at an ordinary bank discount rate of 12%, for 90 days?
I = PRT; I = $5,000(0.12)(90 ÷ 360)
I = $150 (Bank discount)
Proceeds = $5,000 – $150 = $4,850
R =
R or the effective interest rate = 12.4%
R =
R =

43. For the bank discount, use:
Find the Third Party Discount and Proceeds for a Third Party Discount Note
11-3-3
Section 11-3
Promissory Notes
For the bank discount, use:
Third party discount = maturity value of the original note x discount rate x discount period
For the proceeds, use:
Proceeds = maturity value of original note – third-party discount A = P - I

44. Find the proceeds of the note.
An Example…
Section 11-3
Promissory Notes
Mihoc Trailer made a note for $10,000 with Darcy Mihoc, owner, at 9% simple interest based on exact interest and exact time.
The note is made on August 12 and due November 10. Since Mihoc Trailer needs cash, the note is sold to a third party on September 5.
The third-party agrees to accept the note with a 13% annual discount using the banker’s rule.
Find the proceeds of the note.

45. Find the proceeds of the note:
An Example…
Section 11-3
Promissory Notes
Find the proceeds of the note:
To find the proceeds, we find the maturity value of the original note, then the third-party discount.
Exact time is 90 days ( )
I = PRT; I = $10,000(0.09)(90 ÷ 365) = $221.92
MV = P + I = $10,000 + $221.92
MV = $

46. Find the proceeds of the note:
An Example…
Section 11-3
Promissory Notes
Find the proceeds of the note:
Exact time of the discount period is 66 days ( ) between Sept. 5 and Nov. 10.
Ordinary discount rate is 0.13 ÷ 360.
Third party discount: I = PRT
Third party discount = $10,221.92(0.13 ÷ 360)(66)
Third party discount = $243.62
Proceeds: A = P – I
Proceeds = $10, $ = $9,978.30

47. Exercises Set A

48. Principal Interest Time
EXERCISE SET A 2.
Find the simple interest. Round to the nearest cent when necessary.
I = 3,575(0.11)(3) = 1,179.75
Principal
Interest
Time
$3575
11%
3 years ??

49. Principal Interest Time Rate
EXERCISE SET A 4.
Find the rate of annual simple interest.
Principal
Interest
Time
Rate
$800
$124
1 year ??

50. Principal Annual Rate Interest Time
EXERCISE SET A 6.
Find the time period of the loan using the formula for simple interest.
Principal
Annual Rate
Interest
Time
$450
10%
$135 ??

51. Interest Annual Rate Time Principal
EXERCISE SET A 8.
Find the principal, based on simple interest.
Interest
Annual Rate
Time
Principal
$300 3%
2 years ??

52. EXERCISE SET A
10.
A loan for three years with an annual simple interest rate of 9% costs $486 interest. Find the principal.

53. EXERCISE SET A
12.
Write a fraction expressing each amount of time as a part of a year ( 12 months = 1 year ).
Use the banker’s rule to find the interest paid on a loan of $1,200 for 60 days at a simple interest rate of 6% annually.
14.

54. Leap year (add 1 to total) September 30 = day 273 January 27 = day 27
EXERCISE SET A
18.
Use Table 11-1 to find the exact time from the first date to the second date for non–leap years unless a leap year is identified.
January 27, 2008, to September 30, 2008
Leap year (add 1 to total)
September 30 = day 273
January 27 = day 27
= 246 days; 246 days + 1 day = 247 days

55. If a loan is made on the given date, find the date it is due.
EXERCISE SET A
20.
If a loan is made on the given date, find the date it is due.
August 12 for 60 days
August 12 = 224th day
60 days days = 284 days = October 11

56. EXERCISE SET A
22.
Find the discount (ordinary interest) and proceeds on a promissory note for $2,000 made by Barbara Jones on February 10, 2011, and payable to First State Bank on August 10, 2011, with a discount rate of 9%.
August 10 = day 222
February 10 = day 41
Exact time = = 181 days
Discount = 2,000(0.09)(181/360) = 90.50
Proceeds = 2, = 1,909.50

57. EXERCISE SET A
24.
Malinda Levi borrows $12,000 on a 9.5%, 90-day note. On the 30th day, Malinda pays $4,000 on the note. If ordinary interest is applied, what is Malinda’s adjusted principal after the partial payment? What is the adjusted balance due at maturity? What is the amount of interest saved by making the partial payment?
12,000(0.095)(30/360) = 95
4, = 3,905
12, ,905 = 8,095
8,095(0.095)(60/360) =
8, = 8,223.17
The adjusted principal after 30 days is $8,095 and the adjusted balance due at maturity is $8,

58. EXERCISE SET A
24.
Malinda Levi borrows $12,000 on a 9.5%, 90-day note. On the 30th day, Malinda pays $4,000 on the note. If ordinary interest is applied, what is Malinda’s adjusted principal after the partial payment? What is the adjusted balance due at maturity? What is the amount of interest saved by making the partial payment?
Interest with no partial payment:
$12,000(0.095)( 90/360) = $285
Interest with partial payment: $95 + $ = $223.17
Interest saved: $285 - $ = $61.83

59. Bank discount time: 180 - 60 = 120 days Bank discount interest:
EXERCISE SET A
26.
Bennett Sales holds a 180-day note of $7,500 that has an interest rate of 8% annually. After 60 days, the note is sold to a bank at a discount rate of 7% annually. Find the proceeds on the third-party discount note.
I = $7,500(0.08)(180/360) = $300
MV = $7,500 + $300 = $7,800
Bank discount time: = 120 days
Bank discount interest:
$7,800(0.07)(120/360) = $182
Proceed to original payee: $7,800 - $182 = $7,618

60. Practice Test

61. PRACTICE TEST 2.
How much money was borrowed at 12% annually for 6 months if the interest was $90?

62. PRACTICE TEST 4.
A loan of $5,000 at 12% annually requires $1,200 interest. For how long is the money borrowed?

63. PRACTICE TEST 6.
Find the exact time from October 12 to March 28 of the following year (a leap year).
December 31 = day 365
October 12 = day 285
80 days
March 28 = day 87
= 167 days
+ 1 leap day
168 days

64. PRACTICE TEST 8.
Sondra Davis borrows $6,000 on a 10%, 120-day note. On the 60th day, Sondra pays $2,000 on the note. If ordinary interest is applied, what is Sondra’s adjusted principal after the partial payment? What is the adjusted balance due at maturity? What is the amount of interest saved by making the partial payment?
The adjusted principal after 60 days is $4,100 and the adjusted balance due at maturity is $4,168.33

65. PRACTICE TEST 8.
Sondra Davis borrows $6,000 on a 10%, 120-day note. On the 60th day, Sondra pays $2,000 on the note. If ordinary interest is applied, what is Sondra’s adjusted principal after the partial payment? What is the adjusted balance due at maturity? What is the amount of interest saved by making the partial payment?
Interest with no partial payment:
Interest with partial payment: $100 + $68.33 = $168.33
Interest saved: $200  $ = $31.67

66. PRACTICE TEST
10.
A bread machine with a cash price of $188 can be purchased with a one-year loan at 10% annual simple interest. Find the total amount to be repaid.
I = $88(0.1)(1) = $18.80
Total repaid = $188 + $18.80 = $206.80

67. PRACTICE TEST
12.
Find the exact interest on a loan of $850 at 11% annually. The loan was made January 15 and was due March 15.
March 15 = day 74
January 15 = day 15
74  15 = 59 days
I = $850(0.11)(59/365) = $15.11

68. PRACTICE TEST
14.
Find the duration of a loan of $3,000 if the loan required interest of $ and was at a rate of 91/2 % annual simple interest.

69. for 180 days, find the amount of the discount.
PRACTICE TEST
16.
A promissory note using the banker’s rule has a face value of $5,000 and is discounted by the bank at the rate of 14%. If the note is made
for 180 days, find the amount of the discount.

70. PRACTICE TEST
Jerry Brooks purchases office supplies totaling $1,890. He can take advantage of cash terms of 2/10, n/30 if he obtains a short-term loan. If he can borrow the money at 10.5 % annual simple ordinary interest for 20 days, will he save money if he borrows to take advantage of the cash discount? How much will he save?
Find discount amount: 1,890(0.02) = 37.80
Discount price = 1,890  = 1,852.20
I = 1,852.20(0.105)(20/360) = 10.80
1, = 1,863
1,890  1,863 = 27
Yes, he saves $27.
18.

71. PRACTICE TEST
20.
Find the exact interest on a loan of $1,510 at 7 3/4% annual interest for 27 days.