rule of 78?
Robert King
Does anyone understand the "Rule of 78" applied to loans?
Ive made a spreadsheet which shows the amount of principal and interest paid
in each repayment but I'm having trouble calculating the rebate for early
settlement as I dont understand the rules.
My loan is for 15000 over 8 yrs at 8.9% fixed rate.
Monthly Repayments are 216.32.
Hope someone can help.
Many thanks
Robert
Norman Harker
I think you are confusing something with the Rule of 72. (Divide 72 by the
raw percentage and you approximate the years taken to double your money.
I think it unlikely that a crude rule is being applied to your case because
the institution is using a 'sophisticated' annual effective interest rate
conversion to monthly effective equivalent to calculate loan payments. That
is, it is not using 8.9% / 12 but is using (1+8.9%)^(1/12)-1
Now to get to the calculations!
You have a fixed rate loan and the agreement will provide a formula for
calculating the rebate or penalty for early repayment based upon the
prevailing variable loan rate.
In general terms:
1. Calculate the present value of the future repayments using 8.9% as the
discount rate. n.b. This will usually equal the outstanding balance.
2. Then calculate the present value of the future repayments using the
current variable rate (or rate quoted by contract as applicable). Some
times, this is based on the current fixed rate.
The difference between these amounts is the rebate or penalty.
If the rate in 2 is less than the rate in 1, a penalty is paid because the
bank is losing by you terminating the contract at a time when it can only
get a lower rate.
If the rate in 2 is higher than in 1, you get a rebate because the bank is
able to get more.
To go further than that, I need more details on term of loan unexpired and
the rate basis for penalty / rebate calculations. With that the rest is
easy.
In the current environment of recently reduced rates, the calculation will
produce a penalty for recent loans, almost breakeven for loans from 3-4
years ago, rebate for loans taken out over 6/7 years ago.
hth
"Robert King" <KingR...@BTinternet.com> wrote in message
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Alan B. Pearce
>raw percentage and you approximate the years taken to double your money.
He is not confusing it with rule of 72. I understand that the term "rule of
78" has applied to loan rates for many years, especially when calculating
early repayment clawbacks, because the earliest calculation tables published
were based on 78 payment periods. Nowadays it is all done on computer and
the repayment periods can be any number.
I cannot help with the actual formula, just know the background of the name.
Jim Rech
accountants) rule of 78s:
http://www.pine-grove.com/pi09003.htm
--
Jim Rech
Excel MVP
Robert King
Thank you very much for all the info.
I've yet to digest it and try out your suggestions - however I just wanted
to say there is definitely a Rule of 78 - this is what my bank told me - the
calculations are very complicated apparently so the poor "just out of school
mentality" telephone assistant cant help me. Maybe the rule of 72 and 78
refer to the same thing??
I also found this useful calculator on the net but it doesn't give the
rebate info I'm after
http://www.hbguide.com/cgi-bin/rule78_bu.pl
Thanks again
Robert
=============================
"Norman Harker" <nha...@ozemail.com.au> wrote in message
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Robert King
That is a BIG help - now I understand!
All I have to do now is try and work out how to calculate it in my
spreadsheet!
Regards
Robert
========================
"Jim Rech" <jar...@kpmg.com> wrote in message
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Robert King
what my bank told me.
Robert 8^)
"Alan B. Pearce" <A.B.P...@rl.ac.uk> wrote in message
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Norman Harker
Thanks for that and a bit of digging gets it into context.
Fascinating calculations and I have the problem cracked.
78 happens to be the sum of the digits from 1-12 (and I have seen
accountants apply it to depreciation).
This 'rule' appears to be a way of front loading the interest payments.
12/78 for month 1, 11/78 for month 2 etc.
Penalty for early repayment is thus one of having paid an overweighted
proportion of the interest in the early months.
I'd be surprised if this applies to a long term loan but let's see what the
loan agreement says because it is sure to be set out in that document.
Certainly the web example takes a simple interest calculation for 1 year.
Repayments are (Principal + Interest)/12
To amortize the loan, total interest is divided by 78 and 12/78 is deemed
paid in month 1 leaving the balance of (Repayment - 12/78Interest) coming of
the principal owed.
In month 2 11/78 of total interest is deducted from repayment and the
balance comes off the loan....
In this case the loan interest is quoted as simple interest based upon the
amount of original loan. In such cases the compound interest equivalent over
a 1 year loan is approximately double the simple interest rate. With early
repayment, the front loading of interest would make the effective rate even
higher.
In an example, if the simple interest rate is 20%, the compound equivalent
is 41.3%
With repayment after 1 month, the interest that month is (200/78)*12 = 30.77
leaving a reduction in debt of 69.23 thus the loan cash flow is
1000
-100-930.77
giving an annual effective rate of 43.86%
With repayment after 2 months, the interest that month is (200/78)*11 =
28.21 leaving a reduction in debt of 71.79 thus loan cash flow is
1000
-100
-100-858.98
giving an annual effective rate of 43.494%
And so on....
But for an 8 year loan with an effective rate of 8.9%? We know that 8.9% is
effective per annum because the monthly payment of 216.32 checks out.
But that doesn't mean that they don't use a non-traditional amortization
calculation for early repayment.
To use this basis over an 8 year loan:
Sum of digits = (12*8)/2*(12*8)+(12*8)/2 = 4656
Total Interest =PMT((1+8.9%)^(1/12)-1,12*8,15000,0,0)*(12*8)+15000
= -5,766.36
Month 1 interest = 96/4656*-5766.36 = -$118.89
Month 1 principal = 216.32-118.89 = 97.42
Revised debt = -$14,902.58
Month 2 interest = 95/4656*-5766.36 = -117.66
Month 2 principal = 216.32-117.66 = -98.66
Revised debt = -$14,803.92
This is followed through and the proof of the pudding is an end balance of
loan of 0.
The end result is that the declared rate of interest is only 8.9% if you
hold the loan for the full term. At all other points the repayment
calculation makes the effective cost higher.
hth
"Robert King" <KingR...@BTinternet.com> wrote in message
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Norman Harker
I now have this set up in an amortization type schedule that allows varied
inputs of loan, term, interest rate. As with all good amortization
schedules, it's internally self-checking.
E-mail privately if you'd like a copy.
Sees Ya!
"Robert King" <KingR...@BTinternet.com> wrote in message
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Steve Boak
Its amazing to see the flood of responses for anything involving money :-)
<G>
Steve
"Norman Harker" <nha...@ozemail.com.au> wrote in message
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