Lecture Practical business math procedures (11/e) - Chapter 10: Simple interest

Lecture Practical business math procedures (11/e) - Chapter 10: Simple interest. The main contents of the dissertation consist of three main parts: Calculation of simple interest and maturity value, finding unknown in simple interest formula, U.S. rule -- making partial note payments before due date.

Chapter Ten Simple Interest

Learning unit objectives

LU 10-1: Calculation of Simple Interest and Maturity Value

LU 10-3: U.S Rule Making Partial Note Payments before Due Date

LU 10-2: Finding Unknown in Simple Interest Formula

two (principal, rate, or time) are given

and (b) ordinary interest

Maturity Value

Maturity Value (MV) = Principal (P) + Interest (I)

The amount of the loan

(face value)

Cost of borrowing money

Simple Interest Formula

Simple Interest (I) = Principal (P) x Rate (R) x Time (T)

Stated as a

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

Simple Interest Formula

Simple Interest (I) = Principal (P) x Rate (R) x Time (T)

Stated as a

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

Two Methods of Calculating Simple Interest

and Maturity Value

Exact Interest (365 Days)

Time = Exact number of days 365

Method 1: Exact Interest

Used by Federal Reserve banks and the federal government

Method 1:

Exact Interest

Exact Interest (365 Days)

On March 4, Peg Carry borrowed $40,000 at 8% Interest and principal are

due on July 6

I = P x R x T

124 365

MV = P + I

$40,000 + $1,087.12 = $41,087.12 maturity value

Two Methods of Calculating Simple Interest

and Maturity Value

Ordinary Interest (360 Days)

Time = Exact number of days 360

Method 2 : Ordinary Interest (Banker’s Rule)

Method 2 ordinary Interest

Ordinary Interest (360 Days)

On March 4, Peg Carry borrowed $40,000 at 8% Interest and principal

are due on July 6

MV = P + I

$40,000 + $1102.22 = $41,102.22 maturity value

I = P x R x T

124 360

Two Methods of Calculating Simple Interest

and Maturity Value

Exact Interest (365 Days)

MV = P + I

Ordinary Interest (360 Days)

MV = P + I

$15,000 + $326.67 = $15,326.67

On May 4, Dawn Kristal borrowed $15,000 at 8%

Interest and principal are due on August 10

I = P X R X T

98

365

I = P X R X T

98 360

Finding Unknown in Simple Interest

Formula: PRINCIPAL

Principal = Interest Rate x Time

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?

.095 x (90/360)

.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

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

Example: 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 the ordinary interest

method?

$19.48

R = $820.21 x (90/360) = 9.5%

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 (years) = Interest Principle x Rate

Example: 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?

T = $19.48 =

25

$820.21 x 095 .25 x 360 = 90 days

Convert years to days (assume 360

days)

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.

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

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?

$600 76.39 = $523.61

$5,000 – 523.61 = $4,476.39

$5,000 x 11 x 50 =

$76.39

360

U.S Rule (Example, Continued)

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 =

$41.03

360

$800 41.03 = $758.97

$4,476.39 – 758.97 = $3717.42

$3,717.42 x 11 x 10 =

$11.36

360