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Math - Interest Payment - Rule of 78s











































a $400.00 loan is to paid off in 66 monthly payments of $11.62.
The borrower decides to pay off the loan after 18 months of payments.
Use the rule of 78s to find the amount of interest saved.

Pleae help if you can?

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Sep 02, 2011
Interest Payment - Rule of 78s
by: Staff

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Part II

The RULE of 78

The rule of 78 gets its name from the fact that the numbers of the months for 1 year add up to 78

1 - January
2 - February
3 - March
4 - April
5 - May
6 - June
7 - July
8 - August
9 - September
10 - October
11 - November
12 - December

1+2+3+4+5+6+7+8+9+10+11+12 = 78

For your problem, the months for all 66 months add up to 2211:

1+2+3+4+5+ . . . +66 = 2211


The rule of 78 does not follow the amortization table by month (which was calculated above). If you (the borrower) try to pay off the loan early, the rule of 78 allows the lender to require you to pay most of the interest on the entire loan before you pay off the loan itself. This allows the lender to financially penalize you IF YOU TRY TO PAY OFF THE LOAN EARLY.

This is how it works:

For a 1 year loan, the interest you pay in the 1st month = (12/78)*total interest, the 2nd month = (11/78)*total interest, the third month is (10/78)*total interest, etc.

For the 66 month loan in your question, the interest you pay in the 1st month = (66/2211)*total interest, the 2nd month = (65/2211)*total interest, the third month is (64/2211)*total interest, etc.

To find how much interest you would save by PAYING OFF THIS LOAN EARLY (at the end of the 18th month): (1) add the digits for the months remaining, (2) divide that number by 2211, and then (3) multiply the result by the total interest which would be paid if the loan ran for the full 66 months.


Total payments you would make for 66 months if you kept the loan:

66 months x $11.62 per month = $766.92

Total interest payments you would make for 66 months if you kept the loan:

$766.92 - $400 = $366.92


Sum of the reverse digits for the first 18 months:

66+65+64+63+. . .+49 = 1035

Interest paid according the rule of 78

(1035/2211)*366.92 = $171.76


Interest Saved by paying off the loan:

$366.92 - $171.76 = $195.16


The final answer is: by paying off this loan early (at the end of 18th month), you would save $196.16 in future interest payments.



But what should you actually save?

Refer to the amortization table above.

The sum of the future interest payments from the 19th month through the 66th month is:

$217.15

You should save $217.15. The rule of 78 allows the lender to charge an additional $21.99. This is a PENALTY for PAYING OFF the LOAN EARLY.

That is why congress made it illegal for a lender to use the rule of 78 for any loans whose term is longer than 5 years.




Thanks for writing.

Staff
www.solving-math-problems.com


Sep 02, 2011
Interest Payment - Rule of 78s
by: Staff


Part I

The question:

a $400.00 loan is to paid off in 66 monthly payments of $11.62.

The borrower decides to pay off the loan after 18 months of payments.

Use the rule of 78s to find the amount of interest saved.

Pleae help if you can?


The answer:

Before I calculate the answer to your question, there are couple of things you might be interested in:

1) In 1992 Congress outlawed the use of the rule of 78s for closed-end loans (the provisions of the loan cannot be changed) with a term of longer than 5 years.

(You’ll see why this was done when you see the completed calculations.) ref: http://books.google.com/books?id=4mx_7Qgv4TAC&pg=PA131&lpg=PA131&dq=%22Rule+of+78s%22+%2Boutlawed&source=bl&ots=xN8xVgI3wG&sig=KeQxRgBa0uBxjnhZCXRI6QEmFq8&hl=en&ei=YkFhTpCpBIjbiALqn_ibDg&sa=X&oi=book_result&ct=result&resnum=4&ved=0CDEQ6AEwAw#v=onepage&q=%22Rule%20of%2078s%22%20%2Boutlawed&f=false


2) The annual interest rate for this loan ($400 loan with payments of $11.62 per month for 66 months) is slightly over 26.7% on the outstanding balance of the loan. The (fictitious) person who took out this loan is paying 26.7% interest per year.

You can verify the interest rate of 26.7% by using the on-line calculator located at:

http://www.bankrate.com/calculators/mortgages/loan-calculator.aspx

if you try this calculator, enter the following amounts:

Loan amount: $400.00
Loan term: 5.5 years, or 66 months
Interest rate: 26.7% per year

Start Date: enter any date

Click “calculate”


The calculator will calculate the monthly payment of $11.62

(if you’re curious, you can change the interest rate to see how the payment varies)

(1) Click the following link to VIEW the results of the monthly payment calculation; or (2A) highlight and copy the link, then (2B) paste the link into your browser Address bar & press enter:

Use the Backspace key to return to this page:

http://www.solving-math-problems.com/images/payment_calc_2011-09-02.png



To calculate a table which shows the monthly payments, interest paid, etc.:

Click “Show/Calculate Amortization Table”


(1) Click the following link to VIEW the Amortization Table; or (2A) highlight and copy the link, then (2B) paste the link into your browser Address bar & press enter:

Use the Backspace key to return to this page:

http://www.solving-math-problems.com/images/amort_table_2011-09-02.png

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