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 Jans 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. Tims 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. Tims 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 Joes 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 Joes 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