McGraw-Hill/Irwin ©2008 The McGraw-Hill Companies, All Rights Reserved Chapter 10 Simple Interest

10-2 Calculate simple interest and maturity value for months and years Calculate simple interest and maturity value by (a) exact interest and (b) ordinary interest Simple Interest #10 Learning Unit Objectives Calculation of Simple Interest and Maturity Value LU10.1

10-3 Using the interest formula, calculate the unknown when the other two (principal, rate, or time) are given Simple Interest #10 Learning Unit Objectives Finding Unknown in Simple Interest Formula LU10.2

10-4 List the steps to complete the U.S. Rule Complete the proper interest credits under the U.S. Rule Simple Interest #10 Learning Unit Objectives U.S. Rule -- Making Partial Note Payments before Due Date LU10.3

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 a Percent Stated in years Ryan borrowed $30,000. The loan was for 6 months at a rate of 8%. What is interest and maturity value? SI = $30,000 x.08 x 6 = $1, 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 a Percent Stated in years Ryan 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

10-8 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 I = P X R X T $40,000 x.08 x $1, MV = P + I $40,000 + $1, $41, Exact Interest (365 Days) On March 4, Ray 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 $1, MV = P + I $40,000 + $ $41, Ordinary Interest (360 Days) On March 4, Ray borrowed $40,000 at 8%. Interest and principal are due on July 6. Method 2 – Ordinary Interest Bankers 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 $ MV = P + I $15,000 + $ $15, Ordinary Interest (360 Days) On May 4, Ray borrowed $15,000 at 8%. Interest and principal are due on August 10. I = P X R X T $15,000 x.08 x $ MV = P + I $15,000 + $ $15,326.67

10-11 Finding Unknown in Simple Interest Formula - PRINCIPAL Principal = Interest Rate x Time Christina Jones paid the bank $19.48 interest at 9.5% for 90 days. How much did she borrow? $ P =.095 x (90/360) = $ times 90 divided by 360. Do not round answer Interest (I) = Principal (P) x Rate (R) x Time (T) Check: = 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: = x.095 x 90/360 Rate = Interest Principal x Time Christina Jones borrowed $ from the bank. Her interest is $19.48 for 90 days. What rate of interest did Christina pay? $ R = $ 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: = x.095 x 90/360 Time (yrs) = Interest Principle x Rate Christina Jones borrowed $ from the bank. Her interest is $19.48 for 9.5%. How much time does Christina have to repay the loan? $ T = $ x.095 = 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 Darren owes $5,000 on an 11%, 90 day note. On day 50, Darren pays $600 on the note. On day 80, Darren makes an $800 additional payment. Assume a 360- day year. What is Darren’s Adjusted balance after day 50 and after day 80? What is the ending balance due? $5,000 x.11 x 50 = $ $ = $ $5,000 – = $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. Darren owes $5,000 on an 11%, 90 day note. On day 50, Darren pays $600 on the note. On day 80, Darren makes an $800 additional payment. Assume a 360- day year. What is Darren’s Adjusted balance after day 50 and after day 80? What is the ending balance due? $4, x.11 x 30 = $ $ = $ $4, – = $ $3, x.11 x 10 = $ $3, $11.36 = $3,728.78

10-17 Problem 10-16: Solution: 365 Sept $2,300 x.09 x 137/360 = $78.78 Interest $ $2,300 = $2,378.78

10-18 Problem 10-23: Solution: 45 Days $2,000 x.10 x 45 = $ $2, ($700 – $25) $1,325 adjusted balance 75th Day $1,325 x.10 x 30 = $ $1, ($630 – $11.04) $ adjusted balance 120th Day $ x.10 x 45 = $ $ $ ending balance due Total Interest $44.87 ($25 + $ $8.83)

10-19 Problem 10-31: Solution: R = $15 = 12.37% $740 x 59/360

10-20 Problem 10-32: Solution: P = $9 = $ x 60/360