Chapter 10 Simple Interest

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

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

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

Maturity Value (MV) = Principal (P) + Interest (I) Cost of borrowing money The amount of the loan (Face value)

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 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

Two Methods of Calculating Simple Interest and Maturity Value On March 4, Peg Carry borrowed $40,000 at 8%. Interest and principal are due on July 6. Method 1 – Exact Interest Used by Federal Reserve banks and the federal government Exact Interest (365 Days) I = P X R X T $40,000 x .08 x 124 365 $1,087.12 MV = P + I $40,000 + $1,087.12 $41,087.12 Exact Interest (365 Days) Time = Exact number of days 365

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) I = P X R X T $40,000 x .08 x 124 360 $1,102.22 MV = P + I $40,000 + $1102.22 $41,102.22 Ordinary Interest (360 Days) Bankers Rule Time = Exact number of days 360

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) Ordinary Interest (360 Days) I = P X R X T $15,000 x .08 x 98 365 $322.19 MV = P + I $15,000 + $322.19 $15,322.19 I = P X R X T $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

Finding Unknown in Simple Interest Formula - RATE 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% 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 - TIME Time (yrs) = Interest Principle x Rate $19.48 . T = $820.21 x .095 = .25 .25 x 360 = 90 days 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? 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

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 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? 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

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 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 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. $3,717.42 x .11 x 10 = $11.36 360 $3,717.42 + $11.36 = $3,728.78