Chapter 10

1. Chapter 10 Simple Interest

2. #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

3. #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

4. #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

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

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 = $1,200 12 MV = $30,000 + $1,200 = $31,200

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

8. Two Methods of Calculating Simple Interest and Maturity Value On March 4, Ray 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

9. Two Methods of Calculating Simple Interest and Maturity Value Method 2 – Ordinary Interest Bankers Rule On March 4, Ray 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

10. Two Methods of Calculating Simple Interest and Maturity Value On May 4, Ray 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

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? $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

12. Finding Unknown in Simple Interest Formula - RATE Rate = Interest Principal x Time Christina Jones borrowed $820.21 from the bank. Her interest is $19.48 for 90 days. What rate of interest did Christina pay? $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

13. Finding Unknown in Simple Interest Formula - TIME Time (yrs) = Interest Principle x Rate Christina Jones borrowed $820.21 from the bank. Her interest is $19.48 for 9.5%. How much time does Christina have to repay the loan? $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

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

15. U.S. Rule - Example 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? 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

16. U.S. Rule - Example 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? $4,476.39 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

17. Problem 10-16: Solution: 365 Sept. 12 -255 110 + 27 137 $2,300 x .09 x 137/360 = $78.78 Interest $78.78 + $2,300 = $2,378.78

18. Problem 10-23: Solution: • 75th Day • $1,325 x .10 x 30 = $11.04 • 360 • $1,325 • -618.96 ($630 – $11.04) • $706.04 adjusted balance • 45 Days • $2,000 x .10 x 45 = $25.00 • 360 • $2,000 • -675 ($700 – $25) • $1,325 adjusted balance 120th Day $706.04 x .10 x 45 = $8.83 360 $706.04 +8.83 $714.87 ending balance due Total Interest $44.87 ($25 + $11.04 + $8.83)

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

20. Problem 10-32: Solution: P = $9 = $540 .10 x 60/360