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 McGrawHill/Irwin Copyright © 2014 by The McGrawHill Companies, Inc. All rights reserved Learning unit objectives LU 10-1: Calculation of Simple Interest and Maturity Value Calculate simple interest and maturity value for months and years Calculate simple interest and maturity value by (a) exact interest and (b) ordinary interest LU 10-2: Finding Unknown in Simple Interest Formula Using the interest formula, calculate the unknown when the other two (principal, rate, or time) are given LU 10-3: U.S Rule Making Partial Note Payments before Due Date List the steps to complete the U.S Rule Complete the proper interest credits under the U.S Rule 102 Maturity Value Maturity Value (MV) = Principal (P) + Interest (I) The amount of the loan (face value) Cost of borrowing money 103 Simple Interest Formula Simple Interest (I) = Principal (P) x Rate (R) x Time (T) Stated as a Percent Stated in Years Example: Jan Carley borrowed $30,000 for office furniture The loan was for months at an annual interest rate of 8% What are Jan’s interest and maturity value? = $30,000 x 08 x 12 = $1,200 interest MV = $30,000 + $1,200 = $31,200 maturity value 104 Simple Interest Formula Simple Interest (I) = Principal (P) x Rate (R) x Time (T) Stated as a Percent Stated in years Example: Jan borrowed $30,000 The loan was for year at a rate of 8% What is interest and maturity value? I = $30,000 x 08 x = $2,400 interest MV = $30,000 + $2,400 = $32,400 maturity value 105 Two Methods of Calculating Simple Interest and Maturity Value Method 1: Exact Interest Used by Federal Reserve banks and the federal government Exact Interest (365 Days) Time = Exact number of days 365 106 Method 1: Exact Interest On March 4, Peg Carry borrowed $40,000 at 8% Interest and principal are due on July Exact Interest (365 Days) I=PxRxT $40,000 x 08 x 124= $1,087.12 interest 365 MV = P + I $40,000 + $1,087.12 = $41,087.12 maturity value 107 Two Methods of Calculating Simple Interest and Maturity Value Method : Ordinary Interest (Banker’s Rule) Ordinary Interest (360 Days) Time = Exact number of days 360 108 Method ordinary Interest On March 4, Peg Carry borrowed $40,000 at 8% Interest and principal are due on July Ordinary Interest (360 Days) I=PxRxT $40,000 x 08 x 124= $1,002.22 interest 360 MV = P + I $40,000 + $1102.22 = $41,102.22 maturity value 109 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 Ordinary Interest (360 Days) I=PXRXT 98= $322.19 interest 365 MV = P + I $15,000 + $322.19 = $15,322.19 $15,000 x 08 x 98 = $326.67 interest 360 MV = P + I $15,000 + $326.67 = $15,326.67 1010 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? P = $19.48 095 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 1011 Finding Unknown in Simple Interest Formula: RATE 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% Interest (I) = Principal (P) x Rate (R) x Time (T) Check 19.48 = 820.21 x 095 x 90/360 1012 Finding Unknown in Simple Interest Formula: TIME 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 = 25 $19.48 = $820.21 x 095 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 1013 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 1014 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 Calculate interest on principal from date of loan to date of first principal payment Step Apply partial payment to interest due Subtract remainder of payment from principal $5,000 x 11 x $76.39 50 = 360 $600 76.39 = $523.61 $5,000 – 523.61 = $4,476.39 1015 U.S Rule (Example, Continued) 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 Calculate interest on adjusted balance that starts from previous payment date and goes to new payment date Then apply Step Step At maturity, calculate interest from last partial payment Add this interest to adjusted balance $4,476.39 x 11 x $41.03 30 = 360 $800 41.03 = $758.97 $4,476.39 – 758.97 = $3717.42 $3,717.42 x 11 x $11.36 10 = 360 $3,717.42 + $11.36 = $3,728.78 1016 ... objectives LU 1 0-1 : Calculation of Simple Interest and Maturity Value Calculate simple interest and maturity value for months and years Calculate simple interest and maturity value by (a) exact interest. .. ordinary interest LU 1 0-2 : Finding Unknown in Simple Interest Formula Using the interest formula, calculate the unknown when the other two (principal, rate, or time) are given LU 1 0-3 : U.S Rule... of 8% What are Jan’s interest and maturity value? = $30,000 x 08 x 12 = $1,200 interest MV = $30,000 + $1,200 = $31,200 maturity value 104 Simple Interest Formula Simple Interest (I) = Principal