1. Simple Interest Chapter Ten McGraw-Hill/Irwin
Copyright © 2014 by The McGraw-Hill Companies, Inc. All rights reserved.

2. Learning unit objectives
LU 10-1: Calculation of Simple Interest and Maturity Value
Calculate simple interest and maturity value for months and years.
Calculate simple interest and maturity value by (a) exact interest and (b) ordinary interest.
LU 10-2: Finding Unknown in Simple Interest Formula
Using the interest formula, calculate the unknown when the other two (principal, rate, or time) are given.
LU 10-3: U.S. Rule -- Making Partial Note Payments before Due Date
List the steps to complete the U.S. Rule.
Complete the proper interest credits under the U.S. Rule.

3. Simple Interest
In this chapter, you will study simple interest. The principles discussed apply whether you are paying interest or receiving interest. Let's begin by learning how to calculate simple interest.
To calculate simple interest, we use the following simple interest formula:
In this formula: Interest is the cost of borrowing money which is a percent of the principal for a specific time period;  Principal  is the amount of money that is originally borrowed, loaned or deposited; Rate is expressed as a decimal, fraction, or percent; and Time is expressed in years or a fraction of a year.

4. Maturity Value (MV) = Principal (P) + Interest (I)
Maturity is a term used to refer to the length of time from when a fixed-term debt is issued until it must be redeemed (paid off).
When the interest earned is added to the principal and is paid out to the owner at the end of the period; Maturity Value is the Principal plus Interest of the loan
Maturity Value (MV) = Principal (P) + Interest (I)
The amount of the loan
(face value)
Cost of borrowing
money

5. Simple Interest (I) = Principal (P) x Rate (R) x Time (T)
Example #1
Simple Interest (I) = Principal (P) x Rate (R) x Time (T)
Stated as a
Percent
Stated in Years
Example: Jan Carley borrowed $30,000 for office furniture. The loan was for 6 months at an annual interest rate of 8%. What are Jan’s interest and maturity value?
I = $30,000 x .08 x 6 = $1,200 interest 12
MV = $30,000 + $1,200 = $31,200 maturity value

6. Simple Interest (I) = Principal (P) x Rate (R) x Time (T)
Example# 2
Simple Interest (I) = Principal (P) x Rate (R) x Time (T)
Stated as a
Percent
Stated in years
Example: Jan borrowed $30,000. The loan was for 1 year at a rate of 8%. What is interest and maturity value?
I = $30,000 x .08 x 1 = $2,400 interest
MV = $30,000 + $2,400 = $32,400 maturity value

7. Two Methods of Calculating Simple Interest and Maturity Value
Method 1: Exact Interest
Used by Federal Reserve banks and the federal government
Exact Interest (365 Days)
Time = Exact number of days
365

8. Method 2 ordinary Interest
Method 2 : Ordinary In (Banker’s Rule)
Ordinary Interest (360 Days)
Time = Exact number of days
360

9. Method 1: Exact Interest
On March 4, Peg Carry borrowed $40,000 at 8%. Interest and principal are due on July 6.
Exact Interest (365 Days)
I = P x R x T
124
365
$40,000 x .08 x
= $1, interest
MV = P + I
$40,000 + $1, = $41, maturity value

10. Method 2 ordinary Interest
On March 4, Peg Carry borrowed $40,000 at 8%. Interest and principal are due on July 6.
Ordinary Interest (360 Days)
I = P x R x T
124
360
$40,000 x .08 x
= $1, interest
MV = P + I
$40,000 + $ = $41, maturity value

11. More Examples On May 4, Dawn Kristal borrowed $15,000 at 8%.
Interest and principal are due on August 10.
Exact Interest (365 Days)
Ordinary Interest (360 Days)
MV = P + I
$15,000 + $ = $15,322.19
I = P X R X T 98
365
$15,000 x .08 x
= $ interest
I = P X R X T 98
360
$15,000 x .08 x
= $ interest
MV = P + I
$15,000 + $ = $15,326.67

12. Practice Quiz Calculate simple interest (rounded to the nearest cent):
1- $14,000 at 4% for 9 months
2- $25,000 at 7% for 5 years
3- $40,000 at 10.5%  for 19 months
4- On May 4, Dawn Kristal borrowed $15,000 at 8%. Dawn must pay the principal and interest on August 10. What are Dawn's simple interest and maturity value if you use the exact interest method?
5- What are Dawn Kristal's (Problem 4) simple interest and maturity value if you use the ordinary interest method?
For step by step solution watch the video for LU 10-1 ( Go to: McGraw-Hill’s Connect; Assignment # 2; Question 1; Click the eBook & resources options drop down menu; Click Calculating simple interest and maturity value; scroll down to LU10-1 and click

13. Finding Unknown in Simple Interest Formula: PRINCIPAL
In this section we explain how to find the principal, rate, and time of a simple interest loan. In all the calculations, we use 360 days and round only final answers.
Example: Tim Jarvis paid the bank $19.48 interest at 9.5% for 90 days. How much did Tim borrow using the ordinary interest method?
P = $ = $820.21
.095 x (90/360)
.095 times 90 divided by (Do not round answer.)
Interest (I) = Principal (P) x Rate (R) x Time (T)
Check = x .095 x 90/360

14. Finding Unknown in Simple Interest Formula: RATE
Example: Tim Jarvis borrowed $ from a bank. Tim’s interest is $19.48 for 90 days. What rate of interest did Tim pay using the ordinary interest method? $
R = $ x (90/360) = 9.5%
Interest (I) = Principal (P) x Rate (R) x Time (T)
Check = x .095 x 90/360

15. Finding Unknown in Simple Interest Formula: TIME
Example: Tim Jarvis borrowed $ from a bank. Tim’s interest is $19.48 for 90 days. What rate of interest did Tim pay using ordinary interest method?
T = $ = .25.
$ x .095
.25 x 360 = 90 days
Convert years to days (assume 360 days)
Interest (I) = Principal (P) x Rate (R) x Time (T)
Check = x .095 x 90/360

16. Practice Quiz Complete the following (assume 360 days): Principal
For step by step solution watch the video for LU 10-2 ( Go to: McGraw-Hill’s Connect; Assignment # 2; Question 2; Click the eBook & resources options drop down menu; Click finding unknown; scroll down to LU10-2 and click
Principal
Interest rate
Time (days)
Simple interest 1. ? 5%
 90 days
$8,000 2.
$7,000
220 days
 $350 3.
$1,000 8%  ?
 $300

17. U.S. Rule - Making Partial Note Payments before Due Date
Often a person may want to pay off a debt in more than one payment before the maturity date.
The U.S. Rule allows the borrower to receive proper interest credits.
This rule states that any partial loan payment first covers any interest that has built up.
The remainder of the partial payment reduces the loan principal.
Courts or legal proceedings generally use the U.S. Rule.

18. U.S. Rule (Example) $5,000 x .11 x 50 = $76.39
Joe Mill owes $5,000 on an 11%, 90-day note. On day 50, Joe pays $600 on the note. On day 80, Joe makes an $800 additional payment. Assume a 360-day year. What is Joe’s adjusted balance after day 50 and after day 80? What is the ending balance due?
Step 1. Calculate interest on principal from
date of loan to date of first principal payment.
$5,000 x .11 x 50 = $76.39
360
Step 2. Apply partial payment to interest due.
Subtract remainder of payment from principal.
$ = $523.61
$5,000 – = $4,476.39

19. U.S. Rule (Example, Continued)
Joe Mill owes $5,000 on an 11%, 90-day note. On day 50, Joe pays $600 on the note. On day 80, Joe makes an $800 additional payment. Assume a 360-day year. What is Joe’s adjusted balance after day 50 and after day 80? What is the ending balance due?
$4, x .11 x 30 = $41.03
360
$ = $758.97
$4, – = $
Step 3. Calculate interest on adjusted balance that starts from previous payment date and goes to new payment date. Then apply Step 2.
Step 4. At maturity, calculate interest from last partial payment. Add this interest to adjusted balance.
$3, x .11 x = $11.36
360
$3, $11.36 = $3,728.78

20. Practice Quiz
Polly Flin borrowed $5,000 for 60 days at 8%. On day 10, Polly made a $600 partial payment. On day 40, Polly made a $1,900 partial payment. What is Polly's ending balance due under the U.S. Rule (assuming a 360-day year)?
For step by step solution watch the video for LU 10-3 ( Go to: McGraw-Hill’s Connect; Assignment # 2; Question 3; Click the eBook & resources options drop down menu; Click U.S. Rule; scroll down to LU10-3 and click

21. Drill Problem 10-1
Calculate the simple interest and maturity value for the following problem. Round to the nearest cent as needed. LU 10-1(1)
Principal Interest Rate Time Simple Interest Maturity Value
$17, ¼% 18 mo.
$637.50
$17,637.50
Solution:
$17,000 x x 18/12 = $637.50
MV = P I
$17, = $17,000 + $637.50

22. Drill Problem 10-4
Complete the following, using ordinary interest: LU 10-1(2)
Date Date Exact Maturity
Principal Interest Rate Borrowed Repaid Time Interest Value
$1,000 8% March 8 June 9 93
$20.67
$1,020.67
Solution:
Difference = 93 days
T = Exact number of days / 360
$1,000 x x 93/360 = $20.67
MV = P I
$1, = $1, $20.67

23. Drill Problem 10-7
Complete the following, using exact interest: LU 10-1(2)
Date Date Exact Maturity
Principal Interest Rate Borrowed Repaid Time Interest Value
$1,000 8% March 8 June 9 93
$20.67
$1,020.38
Solution:
Difference = 93 days
$1,000 x x 93/365 = $20.38
MV = P I
$1, = $ 1, $20.38

24. Drill Problem 10-10
Solve for the missing item in the following (round to the nearest hundredth as needed): LU 10-2(1)
Time Simple
Principal Interest Rate (months or years ) Interest
$ % ? $100.00
Solution:
$ = 5 years
$ X .05

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