Chapter 10
Simple Interest
McGraw-Hill/Irwin
©2011 The McGraw-Hill Companies, All Rights Reserved
#10
Simple Interest
Learning Unit Objectives
Calculation
of
Simple
Interest
and
LU10.1
Maturity Value
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
10-2
#10
Simple Interest
Learning Unit Objectives
Finding
Unknown
in
Simple
Interest
LU10.2
Formula
1. Using the interest formula, calculate
the unknown when the other two
(principal, rate, or time) are given
10-3
#10
Simple Interest
Learning Unit Objectives
U.S.
Rule
-Making
Partial
Note
LU10.3
Payments before Due Date
1. List the steps to complete the U.S.
Rule
2. Complete the proper interest credits
under the U.S. Rule
10-4
Maturity Value
Maturity Value (MV) = Principal (P) + Interest (I)
The amount of the loan
(Face value)
10-5
Cost of
borrowing
money
Simple Interest Formula
Simple Interest (I) = Principal (P) x Rate (R) x Time (T)
Stated as a
Percent
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
10-6
MV = $30,000 + $1,200 = $31,200
Simple Interest Formula
Simple Interest (I) = Principal (P) x Rate (R) x Time (T)
Stated as a
Percent
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 = $2,400
MV = $30,000 + $2,400 = $32,400
10-7
Two Methods of Calculating Simple Interest
and Maturity Value
Method 1 – Exact Interest
Used by Federal Reserve banks
and the federal government
On March 4, Peg Carry
borrowed $40,000 at 8%.
Interest and principal are due
on July 6.
Exact Interest (365 Days)
Exact Interest (365 Days)
Time = Exact number of days
365
10-8
I=PXRXT
$40,000 x .08 x 124
365
$1,087.12
MV = P + I
$40,000 + $1,087.12
$41,087.12
Two Methods of Calculating Simple Interest
and Maturity Value
Method 2 – Ordinary Interest
Bankers Rule
On March 4, Peg Carry
borrowed $40,000 at 8%.
Interest and principal are due
on July 6.
Ordinary Interest (360 Days)
Ordinary Interest (360 Days)
Bankers Rule
Time = Exact number of days
360
10-9
I=PXRXT
$40,000 x .08 x 124
360
$1,102.22
MV = P + I
$40,000 + $1102.22
$41,102.22
Two Methods of Calculating Simple Interest
and Maturity Value
On May 4, Dawn Kristal borrowed $15,000 at 8%.
Interest and principal are due on August 10.
Exact Interest (365 Days)
I=PXRXT
$15,000 x .08 x 98
365
$322.19
MV = P + I
$15,000 + $322.19
$15,322.19
10-10
Ordinary Interest (360 Days)
I=PXRXT
$15,000 x .08 x 98
360
$326.67
MV = P + I
$15,000 + $326.67
$15,326.67
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 Tim
borrow 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
10-11
Finding Unknown in Simple Interest
Formula - RATE
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?
Interest
Principal x Time
$19.48
.
R = $820.21 x (90/360) = 9.5%
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 - TIME
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)
Interest (I) = Principal (P) x Rate (R) x Time (T)
Check: 19.48 = 820.21 x .095 x 90/360
10-13
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
10-14
U.S. Rule - Example
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 360day 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
$600 - 76.39 = $523.61
$5,000 – 523.61 = $4,476.39
10-15
U.S. Rule - Example
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 360day year. What is Joe’s adjusted balance after day 50 and after day 80? What
is the ending balance due?
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.
10-16
$4,476.39 x .11 x 30 = $41.03
360
$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