chapter 10 simple interest mcgraw-hill/irwin copyright © 2011 by the mcgraw-hill companies, inc....
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Chapter 10
Simple InterestSimple Interest
McGraw-Hill/Irwin Copyright © 2011 by the McGraw-Hill Companies, Inc. All rights reserved.
10-2
1. Calculate simple interest and maturity value for months and years
2. Calculate simple interest and maturity value by (a) exact interest and (b) ordinary interest
Simple Interest#10#10Learning Unit ObjectivesCalculation of Simple Interest and Maturity Value
LU10.1LU10.1
10-3
1. Using the interest formula, calculate the unknown when the other two (principal, rate, or time) are given
Simple Interest#10#10Learning Unit ObjectivesFinding Unknown in Simple Interest Formula
LU10.2LU10.2
10-4
1. List the steps to complete the U.S. Rule
2. Complete the proper interest credits under the U.S. Rule
Simple Interest#10#10Learning Unit ObjectivesU.S. Rule -- Making Partial Note Payments before Due Date
LU10.3LU10.3
10-5
Maturity Value
Maturity Value (MV) = Principal (P) + Interest (I)
The amount of the loan(Face value)
Cost of borrowing
money
10-6
Simple Interest Formula
Simple Interest (I) = Principal (P) x Rate (R) x Time (T)
Stated as aPercent Stated in
years
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?
SI = $30,000 x.08 x 6 = $1,200 12
MV = $30,000 + $1,200 = $31,200
10-7
Simple Interest Formula
Simple Interest (I) = Principal (P) x Rate (R) x Time (T)
Stated as aPercent Stated in
years
Jan borrowed $30,000. The loan was for 1 year at a rate of 8%. What is interest and maturity value?
SI = $30,000 x.08 x 1 = $2,400MV = $30,000 + $2,400 = $32,400
10-8
Two Methods of Calculating Simple Interest and Maturity Value
Exact Interest (365 Days)
Time = Exact number of days 365
Method 1 – Exact InterestUsed by Federal Reserve banksand the federal government
I = P X R X T$40,000 x .08 x 124 365$1,087.12MV = P + I$40,000 + $1,087.12$41,087.12
Exact Interest (365 Days)
On March 4, Peg Carry borrowed $40,000 at 8%. Interest and principal are due on July 6.
10-9
Two Methods of Calculating Simple Interest and Maturity Value
Ordinary Interest (360 Days)
Bankers Rule
Time = Exact number of days 360
I = P X R X T$40,000 x .08 x 124 360$1,102.22MV = P + I$40,000 + $1102.22$41,102.22
Ordinary Interest (360 Days)
On March 4, Peg Carry borrowed $40,000 at 8%. Interest and principal are due on July 6.
Method 2 – Ordinary InterestBankers Rule
10-10
Two Methods of Calculating Simple Interest and Maturity Value
Exact Interest (365 Days)
I = P X R X T$15,000 x .08 x 98 365$322.19MV = P + I$15,000 + $322.19$15,322.19
Ordinary Interest (360 Days)
On May 4, Dawn Kristal borrowed $15,000 at 8%. Interest and principal are due on August 10.
I = P X R X T$15,000 x .08 x 98 360$326.67MV = P + I$15,000 + $326.67$15,326.67
10-11
Finding Unknown in Simple Interest Formula - PRINCIPAL
Principal = Interest Rate x Time
Tim Jarvis paid the bank $19.48 interest at 9.5% for 90 days. How much did Timborrow using ordinary interest method?
$19.48 .P = .095 x (90/360) = $820.21
.095 times 90 divided by 360. Do not round answer
Interest (I) = Principal (P) x Rate (R) x Time (T)
Check: 19.48 = 820.21 x .095 x 90/360
10-12
Finding Unknown in Simple Interest Formula - RATE
Interest (I) = Principal (P) x Rate (R) x Time (T)
Check: 19.48 = 820.21 x .095 x 90/360
Rate = Interest Principal x Time
Tim Jarvis borrowed $820.21 from a bank. Tim’s interest is $19.48 for 90 days. What rate of interest did Tim pay using ordinary interest method?
$19.48 .R = $820.21 x (90/360) = 9.5%
10-13
Finding Unknown in Simple Interest Formula - TIME
Interest (I) = Principal (P) x Rate (R) x Time (T)
Check: 19.48 = 820.21 x .095 x 90/360
Time (yrs) = Interest Principle x Rate
Tim Jarvis borrowed $820.21 from a bank. Tim’s interest is $19.48 for 90 days. What rate of interest did Tim pay using ordinary interest method?
$19.48 .T = $820.21 x .095 = .25
.25 x 360 = 90 days
Convert years to days (assume 360 days)
10-14
U.S. Rule - Making Partial Note Payments before Due Date
Any partial loan payment first covers any interest that has built up. The remainder of
the partial payment reduces the loan principal.
Allows the borrower to receive proper interest credits
10-15
U.S. Rule - Example
Step 1. Calculate interest on principal from date of loan to date of first principal
payment
Step 2. Apply partial payment to interest due. Subtract remainder of payment from
principal
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?
$5,000 x .11 x 50 = $76.39 360
$600 - 76.39 = $523.61$5,000 – 523.61 = $4,476.39
10-16
U.S. Rule - Example
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.
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?
$4,476.39 x .11 x 30 = $41.03360
$800 - 41.03 = $758.97$4,476.39 – 758.97 = $3717.42
$3,717.42 x .11 x 10 = $11.36 360
$3,717.42 + $11.36 = $3,728.78
10-17
Problem 10-16:
Solution: 365Sept. 12 -255
110+ 27 137
$2,300 x .09 x 137/360 = $78.78 Interest$78.78 + $2,300 = $2,378.78
10-18
Problem 10-23:Solution:
45 Days$2,000 x .10 x 45 = $25.00
360
$2,000
-675 ($700 – $25)
$1,325 adjusted balance
75th Day$1,325 x .10 x 30 = $11.04
360
$1,325
-618.96 ($630 – $11.04)
$706.04 adjusted balance
120th Day$706.04 x .10 x 45 = $8.83
360
$706.04
+8.83
$714.87 ending balance due
Total Interest $44.87
($25 + $11.04 + $8.83)
10-19
Problem 10-31:
Solution:
R = $15 = 12.37% $740 x 59/360
10-20
Problem 10-32:
Solution:
P = $9 = $540 .10 x 60/360