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Chapter Sixteen SIMPLE INTEREST Copyright © 2014 by The McGraw-Hill Companies, Inc. All rights reserved.McGraw-Hill/Irwin

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LEARNING UNIT OBJECTIVES 16-2 LU 16-1: Calculation of Simple Interest and Maturity Value 1. List the steps to complete the U.S. Rule. 2. Complete the proper interest credits under the U.S. Rule. LU 16-3: U.S. Rule -- Making Partial Note Payments before Due Date LU 16-2: 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. 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.

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MATURITY VALUE 16-3 Maturity Value (MV) = Principal (P) + Interest (I) The amount of the loan (face value) Cost of borrowing money

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SIMPLE INTEREST FORMULA 16-4 Simple Interest (I) = Principal (P) x Rate (R) x Time (T) Stated as a Percent Stated in Years 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? I = $40,000 x.04 x 6 = $800 interest 12 MV = $40,000 + $800 = $40,000 maturity value

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TWO METHODS OF CALCULATING SIMPLE INTEREST AND MATURITY VALUE 16-5 Exact Interest (365 Days) Time = Exact number of days 365 Method 1: Exact Interest Used by Federal Reserve banks and the federal government

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METHOD 1: EXACT INTEREST Exact Interest (365 Days) On March 4, Joe Bench borrowed $50,000 at 5%. Interest and principal are due on July 6. What is the interest cost and the maturity value? I = P x R x T 124 365 $50,000 x.05 x= $849.32 interest MV = P + I $50,000 + $849.32 = $50,849.32 maturity value 16-6

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TWO METHODS OF CALCULATING SIMPLE INTEREST AND MATURITY VALUE 16-7 Ordinary Interest (360 Days) Time = Exact number of days 360 Method 2 : Ordinary Interest (Banker’s Rule)

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METHOD 2: ORDINARY INTEREST Ordinary Interest (360 Days) 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? MV = P + I $50,000 + $861.11 = $50,861.11 maturity value I = P x R x T 124 360 $50,000 x.05 x= $861.11 interest 16-8

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TWO METHODS OF CALCULATING SIMPLE INTEREST AND MATURITY VALUE 16-9 Exact Interest (365 Days) MV = P + I $50,000 + $849.32 = $50,849.32 Ordinary Interest (360 Days) MV = P + I $50,000 + $861.11 = $50,861.11 I = P X R X T 124 365 $50,000 x.05 x= $849.32 interest I = P X R X T 124 360 $50,000 x.05 x= $861.11 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? Note: By using Method 2, the bank increases its interest by $11.79. $861.11 -$849.32 $ 11.79 Method 2 Method 1

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FINDING UNKNOWN IN SIMPLE INTEREST FORMULA: PRINCIPAL 16-10 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. = $820.21.095 x (90/360).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

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FINDING UNKNOWN IN SIMPLE INTEREST FORMULA: RATE 16-11 Interest (I) = Principal (P) x Rate (R) x Time (T) Check $19.48 = $820.21 x.095 x 90/360 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%

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FINDING UNKNOWN IN SIMPLE INTEREST FORMULA: TIME 16-12 Interest (I) = Principal (P) x Rate (R) x Time (T) Check $19.48 = $820.21 x.095 x 90/360 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 = $19.48 =.25 $820.21 x.095.25 x 360 = 90 days Convert years to days (assume 360 days)

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U.S. RULE - MAKING PARTIAL NOTE PAYMENTS BEFORE DUE DATE 16-13 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.

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U.S. RULE (EXAMPLE) 16-14 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. This is the adjusted balance (principal). 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? $600 -- 27.78 = $572.22 $5,000 – $572.22 = $4,427.78 $5,000 x.04 x 50 = $27.78 360 I = P x R x T

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U.S. RULE (EXAMPLE, CONTINUED) 16-15 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. $4,427.78 x.04 x 30 = $14.76 360 $800 -- $14.76 = $785.24 $4,427.78 – $785.24 = $3,642.54 $3,642.54 x.04 x 10 = $4.05 360 $3,642.54 + $4.05 = $3,646.59 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?

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Simple Interest examples: If you put $600 in a CD at a bank for 6 months at a simple annual rate of 4.9%, how much interest will you earn? How much money.

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