Melissa Borrows $1000 on May 8 at 18.5% simple interest. She pays $500 on July 17 and $400 on September 29. What is her balance on October 31 by the merchant's rule? by the United States rule?
See problem 3.71
Not only are you looking for something to copy, your teacher copied the problem. http://books.google.com/books?id=IKWKPRAu8CAC&pg=PA38&lpg=PA38&dq=simple+interest.+She+pays+$500+on+July+17+and+$400+on+September+29.+What+is+her+balance+on+October+31+by+the+merchant%27s+rule?+by+the+United+States+rule?&source=bl&ots=tcykwNrmR7&sig=rGqz1oM08dmr-_k78oKgu59vtFQ&hl=en&ei=dgroTt2GCs782gWA1Ky9CQ&sa=X&oi=book_result&ct=result&resnum=1&ved=0CB0Q6AEwAA#v=onepage&q=simple%20interest.%20She%20pays%20%24500%20on%20July%2017%20and%20%24400%20on%20September%2029.%20What%20is%20her%20balance%20on%20October%2031%20by%20the%20merchant%27s%20rule%3F%20by%20the%20United%20States%20rule%3F&f=false
Surely I am wrong.
To find Melissa's balance on October 31 using the merchant's rule, we need to calculate the interest on the remaining balance after each payment date and add it to the remaining principal.
First, let's calculate the interest for each payment period.
From May 8 to July 17:
Time = 70 days (May 8 to July 17, inclusive)
Principal = $1000
Rate = 18.5%
Interest = (Principal * Rate * Time) / 365
Interest = (1000 * 0.185 * 70) / 365
Interest = $35.89
Remaining balance after July 17 = Principal - Payment
Remaining balance = $1000 - $500 = $500
From July 17 to September 29:
Time = 74 days (July 17 to September 29, inclusive)
Principal = $500
Rate = 18.5%
Interest = (Principal * Rate * Time) / 365
Interest = (500 * 0.185 * 74) / 365
Interest = $15.04
Remaining balance after September 29 = Principal - Payment
Remaining balance = $500 - $400 = $100
Now, let's calculate the interest from September 29 to October 31:
Time = 32 days (September 29 to October 31, inclusive)
Principal = $100
Rate = 18.5%
Interest = (Principal * Rate * Time) / 365
Interest = (100 * 0.185 * 32) / 365
Interest = $1.61
Finally, the balance on October 31 by the merchant's rule is the remaining balance after September 29 plus the interest from September 29 to October 31:
Balance on October 31 = Remaining balance + Interest
Balance on October 31 = $100 + $1.61
Balance on October 31 = $101.61
Now let's calculate Melissa's balance on October 31 using the United States rule, also known as the simple interest rule.
The United States rule assumes that each payment is applied first to the interest due, and any remaining amount goes towards reducing the principal.
Remaining balance after July 17 = Principal - Payment
Remaining balance = $1000 - $500 = $500
Remaining balance after September 29 = Principal - Payment
Remaining balance = $500 - $400 = $100
Since no further payments were made after September 29, the balance on October 31 remains the same as the remaining balance after September 29.
Balance on October 31 = Remaining balance
Balance on October 31 = $100
By the United States rule, Melissa's balance on October 31 is $100.