How do they work it out?

Of course it shouldn't. Would you still expect to pay 10,920 if you borrowed for 120 months, or 180 months?

And if you were to give the bank 10K at 4% would you expect to get back 10,400 after 60 months?

The rate is an annual rate. The interest is calculated daily (on that day's balance) and, probably, compounded annually.

I can't actually work it out exactly, but my figure is much nearer the finance company's.

tim

10,920.0 )

No, it's 9.2% PER ANNUM (on a declining balance).

I make the outstanding balance around 4010.00 - but there may other charges to include.

It's supposed to be 9.2% per year, not all-in. Just be grateful it's not a flat rate, which would mean interest of 5x9.2% = 46% and hence a total payable of £14,600.

Normally they would specify a nominal rate, and divide by 12 to get the monthly rate. But if I work it out that way, I get a different answer and you should have been paying £208.55 a month. It turns out 9.2 is spot on for the APR. Take the 12th root of 1.092, which is 1.00736, so you're paying 0.736% per month. Plug it into the standard payment formula:

£10,000 * 0.00736 / (1 - 1.00736^-60) and out pops £206.77. Bingo!

You have made 39 payments, so there would have been 21 to go. Take payment formula in reverse:

£206.77 * (1 - 1.00736^-21) / 0.00736 and you get: £4009.62 This is what you theoretically owe immediately after having made the 39th payment. If you pay off on the date the 40th payment would have been due, you'd add a month's interest to that, making £4039.13.

In practice, they may approximate this by using a generalisation of the so-called "rule of 78" which hypothesises that in the case of a

12 month loan you pay 12/78 of the total interest in the first month, 11/78 in the second, etc, and 1/78 in the last month. It all works out because 12+11+10+...+2+1 = 78. So if, say, you were to repay a 12 month loan 2 months early, they should let you off 3/78 of the total interest that would have been payable.

Now, if you have 60 months instead of 12, the rule of 78 becomes a rule of 1830. This is because 1+2+...+60 = 1830.

If (60+59+...+21)/1830 of the total interest payable was deemed to have been included in the first 40 payments, then (20+19+...+2+1)/1830 would have been due in the last 20 payments. If you are no longer borrowing the money for the last 20 months, then 210/1830 of the total interest originally payable (of £2406.20) should now be discounted, which is £276.12. So instead of the total payable being £12406.20, it is now going to be £12130.08. You've already paid £8064.03, so that leaves £4066.05 still due.

Hmm, that doesn't work out either. Still, I think I'm on the right track because £12406.20 - (£4092.35 + £8064.03) = £249.82, so this is how much discount they are actually proposing to allow. That happens to be exactly 190/1830 of the original T.I.P., so it looks like they're one month out in their calculation and are diddling you out of £26.30.

Note that 1+2+...+19 = 190 and 1+2+...+20 = 210.

Thanks to all

ttfn.....Alistair

"Ronald Raygun" wrote

RR, did you forget that the Consumer Credit Act allows a "penalty" of one-or-two (depending on term of loan) months' interest when using the Rule of 78?

Surely if the lender chooses to exercise that option they cannot then claim that they would be applying no penalty.

"Ronald Raygun" wrote

Perhaps, but surely you would also agree that using the Rule of 78 incurs a form of penalty in itself (compared to applying compound interest "properly") ?

In that case, if the lender chooses to apply the Rule of 78, then they also "cannot then claim that they would be applying no penalty" ... ! :-(

When I account for leases I use the rule of 78. I know it's not like having ronald sitting next to me but isn't it reasonably accurate?

The below site explains the rule and the penalty

When I account for leases I use the rule of 78. I know it's not like having ronald sitting next to me but isn't it reasonably accurate?

The below site explains the rule and the penalty

I didn't forget, I just never knew it in the first place. I see the rule is to be abolished. It's amusing how a BBC report got it slightly wrong and referred to "rule 78 of the CCA".

Good point, but it's not necessarily so.

The main purpose of the Ro78 is to achieve a correction of any underpayment of interest arising from the application of a model which is fundamentally based on simple (not compound) interest and on linear reduction of the debt.

The underlying thinking here is that you pay off 1/12 of the principal each month, and that *therefore* 12/78 of the Total Interest Payable must be attributed to the first month, 11/78 to the second, etc. In theory you ought to be paying more interest in the early months and less in the later ones, but for convenience they just let you pay 1/12 of the TIP each month, so that all 12 monthly payments are equal.

Ideally, then, you should also use the Ro78 to calculate the TIP in the first place. This is easy. It's 78/144 of the annual (or 78/12 of the monthly) rate multiplied by the original amount borrowed. Obviously the numbers will be different for terms other than 12 months.

A problem arises when you use the standard formula P = Ar/(1-(1+r)^-n) to calculate the payments, because it fundamentally assumes an exponential rather than a linear model, i.e. it assumes compound interest.

It makes no sense to apply the Ro78, which is based on simple interest, in a scenario itself based on compound interest. It boils down to making clear in the loan agreement whether it is proposed to charge interest on a simple or compound basis. If the former, then it would be perfectly normal to apply the Ro78 to calculate an early repayment settlement figure, but if the latter, to do so would be, as you say, seeking to impose a penalty.

"Ronald Raygun" wrote

Ah, but we already know that the OP's lender *is* using compound interest. So my comment stands! :-)

From your own very good treatise:

"Ronald Raygun" wrote

This, of course, shows that the lender is calculating payments at 9.2%pa using *compound* interest ...

Yes, he probably is, which is why my remark was intended as a general one, and was not directed specifically at the OP's case.

Mind you, we don't *really* know the OP's lender is using CI, we just very strongly suspect it. For all we know, he might actually be charging

9.467% simple, and noting (for compliance purposes) that this corresponds to an APR of 9.2.

"Ronald Raygun" wrote

The APR would *not* be 9.2 if he uses the Rule of 78 on redemption!! :-(

Indeed not, but so what? The APR would not be the basis of the quote, it would only be indicated on the assumption the loan runs to term.

In message , Ronald Raygun writes

It isnt a penalty, it an early repayment charge.

Call it what you like, what matters is whether they said there wasn't going to be one. I think they would be skating on thin ice if they told you when you took out the loan that you could repay early without any penalty, and then tried to sneak in a penalty by calling it a charge, unless they made it equally clear at the outset that there would be a charge in such event.

As ytou have said elsewhere, the 'rule of 78' is just a way of apportioning the interest that would be due, rather than a an extra payment becuase you repay early.

I'm not justifying the 'rule of 78' though, its a relic from before the days of computers and manual repayment tables.

I don't have a problem with the method as such (in circumstances in which it would be reasonable to apply it), but with the practice of chopping a month or two off the discount period. If I repay at the end of *this* month, I don't expect to be charged any interest for

*next* month.

Nothing wrong with relics per se. Just ordered my first ever bifocals last week.

You take this view because you are accustomed to calculating interest based on a set accrual period, in this case, one month. It didnt used to be done like that.

Ah, youve done it then! I know you were considering them. Do women now have 4 breasts?