help with "rule of 78" loan calculation?

Robert_Sterling_3

The "Logic" which lies behind the Rule Of 78 Interest rebate formula is as follows.

Suppose a loan last for 10 years i.e. 120 months.

Then there is an assumption that you repay the capital at the rate of one unit per month.

So
The interest in month 1 is based on 120 units of capital
The interest in month 2 is based on 119 units of capital
The interest in month 3 is based on 118 units of capital
The interest in month 4 is based on 117 units of capital
.
.
.
.
etc
.
.
.
The interest in month n is based on (121-n) units of capital.
.
.
.
The interest in month 118 is based on 3 units of capital
The interest in month 119 is based on 2 units of capital
The interest in month 120 is based on 1 unit   of capital.

The Rule of 78 lets you off all the interest that would have been due, using this model, after you stopped paying.

So initially you are going to pay interest on

120 +119 +118+n 117 +116  ......  +5 +4 +3 +2 +1
units of capital

This happens to add up to  (120*119)/2

If you have m months left then the interest you get let off is on

m + (m-1)  + (m-2) + (m-3)  +  .....  + 3 +2 +1 units of capital

Which happens to add up to  m*(m-1)/2

So the fraction of the total interest you are rebated is

m*(m-1)/2

---

(120*119/2

or

m*(m-1)

---

120*119

And if the loan is for n months then the fraction of Interest rebated is

m*(m-1)

---

n*(n-1)

The amount of Interest rebated is

I *m*(m-1)

---

n*(n-1)

The Consumer Credit Act allows the lender to add a further two months to the period for which payments have been made when calculating the rebate.
The effect of this is that it reduces the value of m used in the above formula by 2 which makes the amount of the rebate lower.



N.B. For a one year loan

The number of months is 12

The number of units of interest charged is

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

Hey presto  The Rule Of 78.

Martinslovechild

Very interesting Robert.

Excellent post.

Robert_Sterling_3

Thank You MLC

Pefki

Hi,

I am looking for advice or confirmation that my redemption figure is correct.

Don't really understand the formulas above and would appreciate if anyone could help.

I took out a loan and these are the details -

LOAN DETAILS
Loan = £15,000 over 60 months.
APR = 10.2%
Interest = £4,322.40
Total Amount Payable = £19,322.40
Monthly Instalment = £322.04

INSURANCE DETAILS (Payment Protection)
Insurance Amount = £3,223.03
Interest = £928.37
Total Amount Payable = 4151.40
APR = 10.2%

Total Amount Repayable (Loan + Insurance) = £23,473.80
Monthly Payment = £391.23 x 60 Months.

We have paid 6 payments = £2,347.38

Today we got our settlement figure = £15,594.37

Our first monthly payment started 3 months after we had received the money, the three months are not included in the 60 month repayment plan as I have the dates of first and last payment.

It just seems a lot of money to settle a loan. I don't understand how I can pay over £2,300 back and still owe them an extra £590 plus the amount originally borrowed. Thats nearly £3,000 for borrowing £15,000 for less than a year.

I would really appreciate some help on this because I feel as if I've been mugged.

Regards

Pefki

Robert_Sterling_3

I am sorry but I have no reason to think that the settlement figure is too high.

A major factor in your current situation is that you signed up to pay 60 monthly payments and only paid 6.
You signed up to pay£23,473.80 but only paid £2347.77



N.B. This is not Finanancial or Legal Advice.

Pefki

I am sorry but I have no reason to think that the settlement figure is too high.

A major factor in your current situation is that you signed up to pay 60 monthly payments and only paid 6.
You signed up to pay£23,473.80 but only paid £2347.77



N.B. This is not Finanancial or Legal Advice.

What I don't understand is how can they continue to charge you interest on the money you have borrowed when you have given it back. Anyway, thanks for the input, I just wanted to make sure I wasn't being ripped off. A lesson learnt here for me.

Robert_Sterling_3

What I don't understand is how can they continue to charge you interest on the money you have borrowed when you have given it back.

You are forgetting that you did not borrow £15,000
You actually borrowed £15,000 + £3223.03
i.e.
£18223.03

You then repaid

£2347.38
Leaving
£15875.65

The settlement figure is

£15,594.37

It looks, at first sight, as if the loan company have had a bad time too.

They have not even got back the money they have loaned to you.

They have in fact let you off the interest for all but about the first six months. i.e. They do not go on charging you interest after the loan has been settled.
This is what they do in accordance with the rule of 78.

So if you are hard done by and the loan company is hard done by what is the explanation.


It may well be that when you were charged £3223.03 insurance  the loan company got some substantial commission.

Do you know if your insurance is quite independent of the loan and continues for a five year period since the premium was all paid on day one.

Alt

What is the easiest method to find out if a loan uses Rule 78 for early redemption or not?

Martinslovechild

The answer may be in the T&C's, but it's probably best to call the loan company up and ask them directly.

Markanderson_2

Hi

I understand rule of 78 over 1 year, if over 2 years is it the same principle, each month is assigned a number (month 1 being 24, month 2 being 23 back to 1. All these totalled = 300 therefore over 2 years the first months interest equals 24/300's of the total?