10. Applying the rule of 78s to determine prepayment penalties Most installment loan contracts that use the add-on method include a prepayment penalty. A prepayment penalty is a special charge assessed to the borrower for paying off a loan early. The rule of 78s method (also called the sum of the digits method) is the most widely used method for calculating a prepayment penalty. Its name derives from the fact that for a one-year loan, the numbers between 1 and 12 representing each month add up to 78 (12 + 11 + 10 + 9 + 8 + 7+ 6 + 5 + 4 + 3 + 2 + 1 = 78). To illustrate the use of the rule of 78s method, consider the following example: Erin Smith from Santa Cruz, California, has borrowed $3,000 for 12 months plus an additional finance charge of $480. She is scheduled to pay equal monthly installments of $290 ($3,480 / 12). Assume that Erin wants to pay off the loan after only 4 months. Step 1: Each month of Erin's loan is assigned a value (12 for the first month, 11 for the second month, 10 for the third month, and so on). Erin has the loan for the first 4 months. Adding up the values for each of the first 4 months gives you the following number: Step 2: According to the rule of 78s method, the lender assumes that a portion of the $480 add- on interest has already been paid. To determine how much interest that Erin has already paid, divide your answer from step 1 (the sum of the values for each month that Erin has the loan) by 78. Then multiply this ratio by the total amount of add-on interest ($480). (Note: Round your answer to the nearest cent.) Interest Paid - (| ] / 78) x $480 = $|
10. Applying the rule of 78s to determine prepayment penalties Most installment loan contracts that use the add-on method include a prepayment penalty. A prepayment penalty is a special charge assessed to the borrower for paying off a loan early. The rule of 78s method (also called the sum of the digits method) is the most widely used method for calculating a prepayment penalty. Its name derives from the fact that for a one-year loan, the numbers between 1 and 12 representing each month add up to 78 (12 + 11 + 10 + 9 + 8 + 7+ 6 + 5 + 4 + 3 + 2 + 1 = 78). To illustrate the use of the rule of 78s method, consider the following example: Erin Smith from Santa Cruz, California, has borrowed $3,000 for 12 months plus an additional finance charge of $480. She is scheduled to pay equal monthly installments of $290 ($3,480 / 12). Assume that Erin wants to pay off the loan after only 4 months. Step 1: Each month of Erin's loan is assigned a value (12 for the first month, 11 for the second month, 10 for the third month, and so on). Erin has the loan for the first 4 months. Adding up the values for each of the first 4 months gives you the following number: Step 2: According to the rule of 78s method, the lender assumes that a portion of the $480 add- on interest has already been paid. To determine how much interest that Erin has already paid, divide your answer from step 1 (the sum of the values for each month that Erin has the loan) by 78. Then multiply this ratio by the total amount of add-on interest ($480). (Note: Round your answer to the nearest cent.) Interest Paid - (| ] / 78) x $480 = $|
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
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Transcribed Image Text:Step 4:
Determine how much of the original amount borrowed remains unpaid. Subtract the
amount of the principal that has been repaid (from step 3) from the original amount
borrowed: (Note: Round your answer to the nearest cent.)
$3,000 (Original Amount Borrowed) - $
(Amount of Principal Repaid) = $
(Principal Left Unpaid)
Step 5: Erin pays off her loan after only 4 months, which is one-third (4/12 = 1/3) of the way
through the loan. Erin might (incorrectly) expect to owe only $2,000 of the original
amount borrowed (the remaining two-thirds of the original amount borrowed). (Note:
Round your answer to the nearest cent.)
However, in reality, Erin still owes $
of the original amount borrowed
(from step 4). Now you can calculate the prepayment penalty as follows:
24
(Amount of Original Loan Unpaid) - $2,000 = $
(Prepayment Penalty)
Transcribed Image Text:10. Applying the rule of 78s to determine prepayment penalties
Most installment loan contracts that use the add-on method include a prepayment penalty. A prepayment penalty is a special charge assessed to the
borrower for paying off a loan early.
The rule of 78s method (also called the sum of the digits method) is the most widely used method for calculating a prepayment penalty. Its name
derives from the fact that for a one-year loan, the numbers between 1 and 12 representing each month add up to 78 (12 + 11 + 10 + 9 + 8 + 7+ 6 +
5+ 4 + 3 + 2 +1 = 78).
To illustrate the use of the rule of 78s method, consider the following example:
Erin Smith from Santa Cruz, California, has borrowed $3,000 for 12 months plus an additional finance charge of $480. She is scheduled
to pay equal monthly installments of $290 ($3,480 / 12). Assume that Erin wants to pay off the loan after only 4 months.
Step 1:
Each month of Erin's loan is assigned a value (12 for the first month, 11 for the second
month, 10 for the third month, and so on). Erin has the loan for the first 4 months. Adding
up the values for each of the first 4 months gives you the following number:
Step 2:
According to the rule of 78s method, the lender assumes that a portion of the $480 add-
on interest has already been paid. To determine how much interest that Erin has already
paid, divide your answer from step 1 (the sum of the values for each month that Erin has
the loan) by 78. Then multiply this ratio by the total amount of add-on interest ($480).
(Note: Round your answer to the nearest cent.)
Interest Paid =
| 78) x $480 = $
Step 3:
After 4 months, Erin has made a total of $1,160 in payments. Subtract the total amount of
interest paid (from step 2) from $1,160. This gives you the amount of the $3,000
originally borrowed that has been repaid. Perform this calculation to determine how much
of the original loan (the principal) has been repaid: (Note: Round your answer to the
nearest cent.)
$1,160 (Total Payments Made) - $
(Interest Paid) = $
(Amount of Original $3,000 Borrowed That Has Been Repaid)
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