Simple Interest PDF

SIMPLE INTEREST Module 1 © McGraw-Hill Education. All rights reserved. Authorized only for instructor use in the classroom. No reproduction...

SIMPLE INTEREST Module 1 © McGraw-Hill Education. All rights reserved. Authorized only for instructor use in the classroom. No reproduction or further distribution permitted without the prior written consent of McGraw-Hill Education.  Learning Unit Objectives 1-1: Calculation of Simple Interest and 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. 1-2: Finding Unknown in Simple Interest Formula 1. Using the interest formula, calculate the unknown when the other two (principal, rate, or time) are given. 1-3: U.S. Rule -- Making Partial Note Payments before Due Date 1. List the steps to complete the U.S. Rule as well as calculate proper interest credits. © McGraw-Hill Education. 16-2  Definition of Terms Lender / Creditor – the person or institution that makes the funds available to those who need it. Borrower – the person or institution that avails of the funds from the lender. Interest AMOUNT– a certain sum of money that the lender charges the borrower for the use of the funds. © McGraw-Hill Education. 16-3 Lender/Borrower © McGraw-Hill Education. 16-4  Maturity Define Maturity is the date on which the life of a transaction or financial instrument ends, after which it must either be renewed, or it will cease to exist. The term is commonly used for deposits, foreign exchange spot, and forward transactions, interest rate and commodity swaps, options, loans and fixed income instruments such as bonds. © McGraw-Hill Education. 16-5  Maturity Value FORMULA: Maturity Value (MV) = Principal (P) + Interest (I) Principal is the amount of the loan (face value) Interest is the cost of borrowing money © McGraw-Hill Education. 16-6  Simple Interest Why do we study simple interest? © McGraw-Hill Education. 16-7  Simple Interest Formula Understanding simple interest is one of the most important and fundamental concepts for mastering your finances. With an understanding of how interest works, you become empowered to make better financial decisions that save your money. The simple interest calculation provides a very basic way of looking at interest. It’s an introduction to the concept of interest in general. In the real world, your interest—whether you’re paying it or earning it. © McGraw-Hill Education. 16-8  Simple Interest Is primarily used for short-term, low-dollar loans and notes, with principal being paid in a lump sum at the end of the loan or note. The principles discussed apply whether you are paying interest or receiving interest. © McGraw-Hill Education. 16-9  Simple Interest Formula Rate – the rate charged by the lender or rate of increase of the investment. - is Stated as a Percent and quoted per annum –Expressed in decimals Time - is stated in Years the sum of money was borrowed or invested. Principal – is the sum of money borrowed or invested. FORMULA: Simple Interest (I) = Principal (P) × Rate (R) × Time (T) © McGraw-Hill Education. 16-10  Simple Interest Formula Simple Interest (I) = Principal (P) × Rate (R) × Time (T) Example: Hope Slater borrowed $40,000 for office furniture. The loan was for 6 months at an annual interest rate of 4%. What are Hope’s interest and maturity value? GIVEN: P= $40,000. R= 4% or.04/12=.0033/month=.0033333x6=2% T= 6 MONTHS=6/12=50% 𝐼𝑛𝑡𝑒𝑟𝑒𝑠𝑡 = $40,000𝑥. 02 = $800 alternative 6 𝐼𝑛𝑡𝑒𝑟𝑒𝑠𝑡 = $40,000 𝑥. 04𝑥 12 = $800.00 [PRT] 𝐼𝑛𝑡𝑒𝑟𝑒𝑠𝑡 = $40,000𝑥. 04𝑥. 05 = $800.00 [PRT] 𝑀𝑎𝑡𝑢𝑟𝑖𝑡𝑦 𝑉𝑎𝑙𝑢𝑒$40,000 + 400.00 = $40,800.00 © McGraw-Hill Education. 16-11  Simple Interest Formula Simple Interest (I) = Principal (P) × Rate (R) × Time (T) Example: Hope Slater borrowed $40,000 for office furniture. The loan was for 6 months at an annual interest rate of 4%. What are Hope’s interest and maturity value? GIVEN: 6 P=$40,00.0 𝐼 = $40,000𝑥. 04𝑥 12 R= 4% or.04 𝐼 = $800 T= 6month/12months=.5 𝑀 = $40,000 + 800 = $40,800.00 © McGraw-Hill Education. 16-12  Simple Interest Formula Simple Interest (I) = Principal (P) × Rate (R) × Time (T) Example: Hope Slater borrowed $40,000 for office furniture. The loan was for 6 months at an annual interest rate of 4%. What are Hope’s interest and maturity value? 6 I = $40,000 .04  MV = $40,000 + $800 = $40,800 maturity value 𝐼 = 40,000𝑥. 00333333𝑥6 = 800 © McGraw-Hill Education. 16-13  Two Methods of Calculating Simple Interest and Maturity Value (Method 1) Method 1: Exact Interest Used by Federal Reserve banks and the federal government Exact Interest (365 Days) © McGraw-Hill Education. 16-14  Two Methods of Calculating Simple Interest and Maturity Value (Method 1) Method 1: Exact Interest Used by Federal Reserve banks and the federal government Exact Interest (365 Days) Exact number of days Time = 365 © McGraw-Hill Education. 16-15  Two Methods of Calculating Simple Interest and Maturity Value (Method 2) Method 2 : Ordinary Interest (Banker’s Rule) Ordinary Interest (360 Days) Exact number of days Time = 360 © McGraw-Hill Education. 16-16 Ordinary Interest vs. Exact Interest On March 4, Joe Bench borrowed $50,000 at 5%. Interest and principal are due on July 6. What are the interest cost and maturity value? Ordinary Interest (360 Days) I = P × R × T; M=P+I © McGraw-Hill Education. 16-17 Ordinary Interest vs. Exact Interest On March 4, Joe Bench borrowed $50,000 at 5%. Interest and principal are due on July 6. What are the interest cost and maturity value? Ordinary Interest (360 Days) I = P × R × T; M=P+I GIVEN: 124 P=$50,000 𝐼 𝑜𝑟𝑑𝑖𝑛𝑎𝑟𝑦 = $50,000𝑥. 05𝑥 360 R= 5% or.05 𝐼 = $861.11 T=124 360 𝑀𝑉 = $50,000 + 861.11 = $50,861.11 124 𝐼𝐸𝑥𝑎𝑐𝑡 = $50,000𝑥. 05𝑥 365 𝐼𝐸𝑥𝑎𝑐𝑡 = $849.32 𝑀𝑉 = $50,000 + 849.32 = $50,849.32 © McGraw-Hill Education. 16-18 On March 4, Joe Bench borrowed $50,000 at 5%. Interest and principal are due on July 6. What are the interest cost and maturity value? Ordinary Interest (360 Days) I=P×R×T the number of days in each month. March 4 – July 6 January 31 July 31 March 31-4 27 February 28 August 31 April 30 March 31 September 30 May 31 April 30 October 31 June 30 May 31 November 30 July 6 June 30 December 31 No. of days 124 Solution: = _124_days © McGraw-Hill Education. 16-19 On March 4, Joe Bench borrowed $50,000 at 5%. Interest and principal are due on July 6. What are the interest cost and maturity value? Ordinary Interest (360 Days) I=P×R×T the number of days in each month. March 4 – July 6 January 31 July 31 March 31-4 27 February 28 August 31 April 30 March 31 September 30 May 31 April 30 October 31 June 30 May 31 November 30 July 6 June 30 December 31 No. of days 124 Solution: = _124 days © McGraw-Hill Education. 16-21 Ordinary Interest vs. Exact Interest On March 4, Joe Bench borrowed $50,000 at 5%. Interest and principal are due on July 6. What are the interest cost and maturity value? Ordinary Interest (360 Days) I=P×R×T 124 $50,000 .05  = $861.11 interest 360 MV = P + I $50,000 + $861.11 = $50,861.11 maturity value MV (exact interest)= P + I $50,000 + $849.32 = $50,849.32 maturity value © McGraw-Hill Education. 16-21  Two Methods of Calculating Simple Interest and Maturity Value On March 4, Joe Bench borrowed $50,000 at 5%. Interest and principal are due on July 6. What are the interest cost and maturity value? Exact Interest (365 Days) Ordinary Interest (360 Days) I=P×R×T I=P×R×T © McGraw-Hill Education. 16-22  Two Methods of Calculating Simple Interest and Maturity Value On March 4, Joe Bench borrowed $50,000 at 5%. Interest and principal are due on July 6. What are the interest cost and maturity value? Exact Interest (365 Days) Ordinary Interest (360 Days) I=P×R×T I=P×R×T 124 124 $50,000 .05  = $849.32 interest $50,000 .05  = $861.11 interest 365 360 ORDINARY 861.11 EXACT 849.32 11.79 © McGraw-Hill Education. 16-23  Two Methods of Calculating Simple Interest and Maturity Value On March 4, Joe Bench borrowed $50,000 at 5%. Interest and principal are due on July 6. What are the interest cost and maturity value? Exact Interest (365 Days) Ordinary Interest (360 Days) I=P×R×T I=P×R×T 124 124 $50,000 .05  = $849.32 interest $50,000 .05  = $861.11 interest 365 360 © McGraw-Hill Education. 16-24 Finding Unknown in Simple Interest Formula: PRINCIPAL © McGraw-Hill Education. 16-25  Finding Unknown in Simple Interest Formula: PRINCIPAL 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? 𝐼𝑛𝑡𝑒𝑟𝑒𝑠𝑡 𝑃𝑟𝑖𝑛𝑐𝑖𝑝𝑎𝑙 = 𝑅𝑎𝑡𝑒 𝑥 𝑇𝑖𝑚𝑒 GIVEN: PRINCIPAL - ? 19.48 𝑃𝑟𝑖𝑛𝑐𝑖𝑝𝑎𝑙 = = $820.21 RATE- 9.5%;.095.095 𝑥 90 90 360 TIME- 360 © McGraw-Hill Education. 16-26 Finding Unknown in Simple Interest Formula: PRINCIPAL 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? 𝐼𝑛𝑡𝑒𝑟𝑒𝑠𝑡 𝑃𝑟𝑖𝑛𝑐𝑖𝑝𝑎𝑙 = 𝑅𝑎𝑡𝑒 𝑥 𝑇𝑖𝑚𝑒 © McGraw-Hill Education. 16-27 Finding Unknown in Simple Interest Formula: PRINCIPAL 𝐼𝑛𝑡𝑒𝑟𝑒𝑠𝑡 𝑃𝑟𝑖𝑛𝑐𝑖𝑝𝑎𝑙 = 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? $19.48 P= = $820.21.095  (90 360).095 times 90 divided by 360. (Do not round answer.) Interest (I) = Principal (P) × Rate (R) × Time (T) Check $19.48 = $820.21 ×.095 × 90/360 © McGraw-Hill Education. 16-28 Finding Unknown in Simple Interest Formula: RATE 𝐼𝑛𝑡𝑒𝑟𝑒𝑠𝑡 𝑅𝑎𝑡𝑒 = 𝑃𝑟𝑖𝑛𝑐𝑖𝑝𝑎𝑙 𝑥 𝑇𝑖𝑚𝑒 © McGraw-Hill Education. 16-29 Finding Unknown in Simple Interest Formula: 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 the ordinary interest method? GIVEN: Interest Rate = P=$820.21 Principal  Time T=90/360 I=$19.48 R=? © McGraw-Hill Education. 16-30 Finding Unknown in Simple Interest Formula: 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 the ordinary interest method? Interest Rate = Principal  Time GIVEN: P=$820.21 T=90/360 $19.48 𝑅𝑎𝑡𝑒 = =.095𝑜𝑟 9.5% I=$19.48 $820.21 𝑥 90 R=? 360 © McGraw-Hill Education. 16-31 Finding Unknown in Simple Interest Formula: RATE Interest Rate = Principal  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 = = 9.5% $820.21  (90 360) Interest (I) = Principal (P) × Rate (R) × Time (T) Check $19.48 = $820.21 ×.095 × 90/360 © McGraw-Hill Education. 16-32 Finding Unknown in Simple Interest Formula: TIME 𝐼𝑛𝑡𝑒𝑟𝑒𝑠𝑡 𝑇𝑖𝑚𝑒 𝑦𝑒𝑎𝑟𝑠 = 𝑃𝑟𝑖𝑛𝑐𝑖𝑝𝑎𝑙 𝑥 𝑅𝑎𝑡𝑒 © McGraw-Hill Education. 16-33 Finding Unknown in Simple Interest Formula: TIME 𝐼𝑛𝑡𝑒𝑟𝑒𝑠𝑡 𝑇𝑖𝑚𝑒 𝑦𝑒𝑎𝑟𝑠 = 𝑃𝑟𝑖𝑛𝑐𝑖𝑝𝑎𝑙 𝑥 𝑅𝑎𝑡𝑒 Example: Tim Jarvis borrowed $820.21 from a bank. Tim’s interest is $19.48 with 9.5%. What time using ordinary interest method? © McGraw-Hill Education. 16-34 Finding Unknown in Simple Interest Formula: TIME 𝐼𝑛𝑡𝑒𝑟𝑒𝑠𝑡 𝑇𝑖𝑚𝑒 𝑦𝑒𝑎𝑟𝑠 = 𝑃𝑟𝑖𝑛𝑐𝑖𝑝𝑎𝑙 𝑥 𝑅𝑎𝑡𝑒 Example: Tim Jarvis borrowed $820.21 from a bank. Tim’s interest is $19.48. What rate of interest did Tim pay using ordinary interest method? $19.48 𝑇= =.25 $820.21𝑥. 095 Convert years to days (assume 360 days).25 x 360 = 90 days Interest (I) = Principal (P) × Rate (R) × Time (T) Check $19.48 = $820.21 ×.095 × 90/360 © McGraw-Hill Education. 16-35  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. © McGraw-Hill Education. 16-36  U.S. Rule Example (1 of 2) Jeff Edsell owes $5,000 on a 4%, 90-day note. On day 50, Jeff pays $600 on the note. On day 80, Jeff makes an $800 additional payment. Assume a 360-day year. What is Jeff’s adjusted balance after day 50 and after day 80? What is the ending balance due? © McGraw-Hill Education. 16-37  U.S. Rule Example (1 of 2) Jeff Edsell owes $5,000 on a 4%, 90-day note. On day 50, Jeff pays $600 on the note. On day 80, Jeff makes an $800 additional payment. Assume a 360-day year. What is Jeff’s adjusted balance after day 50 and after day 80? What is the ending balance due? 10th 20th 30th 40th 50th 60th 70th 80th 90th 10days $600 $800 © McGraw-Hill Education. 16-38  U.S. Rule Example (1 of 2) Jeff Edsell owes $5,000 on a 4%, 90-day note. On day 50, Jeff pays $600 on the note. On day 80, Jeff makes an $800 additional payment. Assume a 360-day year. What is Jeff’s adjusted balance after day 50 and after day 80? What is the ending balance due? GIVEN: PRINCIPAL: $5,000 INTEREST RATE: 4%;.04 TERM: 1st payment: 50th day = $600 2nd payment: 80th day = $800 BALANCE DUE: ? © McGraw-Hill Education. 16-39  U.S. Rule Example (1 of 2) Step 1. Calculate interest on principal from date of loan to date of first principal payment. I=P×R×T BALANCE DUE: ? Beginning Interest Amt. Principal payment Ending Value Value Payment (1) x.04 (2) – (3) (1) – (4) (Pricipal) (2) (3) (4) (5) (1) 5,000 600 27.78 572.22 4,427.78 4,427.78 800 14.75 785.24 3,642.54 50 30 𝐼5𝑂𝑡ℎ = 5000𝑥. 04𝑥 = 27.78 𝐼8𝑂𝑡ℎ = 4,427.78𝑥. 04𝑥 = 360 360 80-50=30 days © McGraw-Hill Education. 16-41  U.S. Rule Example (1 of 2) Jeff Edsell owes $5,000 on a 4%, 90-day note. On day 50, Jeff pays $600 on the note. On day 80, Jeff makes an $800 additional payment. Assume a 360-day year. What is Jeff’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. I=P×R×T © McGraw-Hill Education. 16-41  U.S. Rule Example (1 of 2) Jeff Edsell owes $5,000 on a 4%, 90-day note. On day 50, Jeff pays $600 on the note. On day 80, Jeff makes an $800 additional payment. Assume a 360-day year. What is Jeff’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. I=P×R×T 50 $5,000 .04  = $27.78 360 © McGraw-Hill Education. 16-42  U.S. Rule Example (1 of 2) Jeff Edsell owes $5,000 on a 4%, 90-day note. On day 50, Jeff pays $600 on the note. On day 80, Jeff makes an $800 additional payment. Assume a 360-day year. What is Jeff’s adjusted balance after day 50 and after day 80? What is the ending balance due? Step 2. Apply partial payment to interest due. Subtract remainder of payment from principal. This is the adjusted balance (principal). © McGraw-Hill Education. 16-43  U.S. Rule Example (1 of 2) Jeff Edsell owes $5,000 on a 4%, 90-day note. On day 50, Jeff pays $600 on the note. On day 80, Jeff makes an $800 additional payment. Assume a 360-day year. What is Jeff’s adjusted balance after day 50 and after day 80? What is the ending balance due? Step 2. Apply partial payment to interest due. Subtract remainder of payment from principal. This is the adjusted balance (principal). $600 − 27.78 = $572.22 $5,000 − $572.22 = $4,427.78 © McGraw-Hill Education. 16-44  U.S. Rule Example (2 of 2) Step 3. Calculate interest on adjusted balance that starts from previous payment date and goes to new payment date. Then apply Step 2. 30 $4,427.78 .04  = $14.76 360 $800 − $14.76 = $785.24 $4,427.78 − $785.24 = $3,642.54 Step 4. At maturity, calculate interest from last partial payment. Add this interest to adjusted balance. 10 $3,642.54 .04  = $4.05 360 $3,642.54 + $4.05 = $3,646.59 the amount due on 90th © McGraw-Hill Education. 16-45  Problem 16-1 Calculate the simple interest and maturity value for the following problem. Round to the nearest cent as needed. Learning Unit 16-1(1) Principal Interest Rate Time Simple Interest Maturity Value $7,800 4¼% 18 mo. $497.25 $8,297.25 Solution: $7,800 ×.0425 × 18/12 = $497.25 MV = P + I $8,297.25 = $7,800.00 + $497.25 © McGraw-Hill Education. 16-46  Problem 16-4 Complete the following, using ordinary interest: Learning Unit 16-1(2) Interest Date Date Maturity Principal Exact Time Interest Rate Borrowed Repaid Value $1,000 8% March 8 June 9 $1,020.67 Solution: © McGraw-Hill Education. 16-47  Calculating the exact number of days Interest Date Date Maturity Principal Exact Time Interest Rate Borrowed Repaid Value $1,000 8% March 8 June 9 93 DAYS 20.67 $1,020.67 the number of days in each month. March 8 - June 9 January 31 July 31 March 8 31 - 8 23 February 28 August 31 April 30 30 March 31 September 30 May 31 31 April 30 October 31 June 9 9 May 31 November 30 No. of days 93 June 30 December 31 Solution: 23+30+31+9= 93 days © McGraw-Hill Education. 16-48  Problem 16-4 Complete the following, using ordinary interest: Learning Unit 16-1(2) Interest Date Date Maturity Principal Exact Time Interest Rate Borrowed Repaid Value $1,000 8% March 8 June 9 93 DAYS $20.67 $1,020.67 Solution: 67 160 Difference = 93 days T = Exact number of days / 360 $1,000 ×.08 × 93/360 = $20.67 MV = P + I $1,020.67 = $1,000.00 + $20.67 © McGraw-Hill Education. 16-49  Calculating the exact number of days Interest Date Date Maturity Principal Exact Time Interest Rate Borrowed Repaid Value $1,000 8% March 8 June 9 93 $20.67 $1,020.67 the number of days in each month. January 31 July 31 March 8 June 9 February 28 August 31 January January March 31 September 30 February February April 30 October 31 March March May 31 November 30 No. of days April June 30 December 31 May Solution: June No. of days 67 160 Difference = 93 days © McGraw-Hill Education. 16-50  Problem 16-7 Complete the following, using exact interest: Learning Unit 16-1(2) Interest Date Date Maturity Principal Exact Time Interest Rate Borrowed Repaid Value $1,000 8% March 8 June 9 93 $20.38 $1,020.38 Solution: 67 160 Difference = 93 days $1,000 ×.08 × 93/365 = $20.38 MV = P + I $1,020.38 = $1,000.00 + $20.38 © McGraw-Hill Education. 16-51  Problem 16-10 Solve for the missing item in the following (round to the nearest hundredth as needed): Learning Unit 16-2(1) Principal Interest Rate Time (months or years) Simple Interest $400 5% ? $100.00 Solution: $100 = 5 years $400 .05 © McGraw-Hill Education. 16-52  Maturity Value (MV) = Principal (P) + Interest (I) Simple Interest (I) = Principal (P) × Rate (R) × Time (T) 𝐼𝑛𝑡𝑒𝑟𝑒𝑠𝑡 𝑃𝑟𝑖𝑛𝑐𝑖𝑝𝑎𝑙 = 𝑅𝑎𝑡𝑒 𝑥 𝑇𝑖𝑚𝑒 𝐼𝑛𝑡𝑒𝑟𝑒𝑠𝑡 𝑅𝑎𝑡𝑒 = 𝑃𝑟𝑖𝑛𝑐𝑖𝑝𝑎𝑙 𝑥 𝑇𝑖𝑚𝑒 𝐼𝑛𝑡𝑒𝑟𝑒𝑠𝑡 𝑇𝑖𝑚𝑒 𝑦𝑒𝑎𝑟𝑠 = 𝑃𝑟𝑖𝑛𝑐𝑖𝑝𝑎𝑙 𝑥 𝑅𝑎𝑡𝑒 © McGraw-Hill Education. All rights reserved. Authorized only for instructor use in the classroom. No reproduction or further distribution permitted without the prior written consent of McGraw-Hill Education. 16-53  End of Presentation © McGraw-Hill Education. All rights reserved. Authorized only for instructor use in the classroom. No reproduction or further distribution permitted without the prior written consent of McGraw-Hill Education. 16-54