Another Halifax "Lifetime of Balance" Question

To mention an APR they have to assume a particular repayment pattern, and of course by law they must mention an APR so they will assume a particular payment pattern. It's just that with such a great rate you might not wish to conform to whatever "typical" pattern they pluck out of the air.

But if you're going to compare like with like, use the "pa" rates, divide by 12, and add 1 to get "f" (so 4.95% pa would give 1.004125). The assumption is that you plan to repay in fixed instalments over N months. For your Halifax deal, the monthly payments should work out at £10,200 * (f-1) / (1 - f^-N), while for the competing fixed rate loan deal, it would be £10,000 * (g-1) / (1-g^-N), where "g" corresponds to "f", but is worked out from the other loan's "pa" rate in the same way.

As a first approximation, I'd say you'll break even if g-1 is 102% of f-1, i.e. if the loan rate is 5.049%pa. 5.8% apr is rather more than thet, so it looks like Halifax offer is the better deal.

"Ronald Raygun" wrote

Eh? Are you sure about that?

Suppose both factors were very close to one -- eg f = 1.000000100 & g 1.000000102 (almost zero interest). In that case, you'd say that this is the break-even point? In both cases the interest, even over 4-5 years, is negligible. But the Halifax deal would charge 2% of 10K up-front, ie 200. Sounds much worse to me! [In the case of near-zero interest.]

I'd say that, if the debt were paid uniformly over around 4 years, then 2% of initial amount is about 4% of average amount, which is therefore equivalent to about 1%pa more (just like 1% APR is close to 0.5%pa flat, which over 4 years is 2% total). So 2% + 4.95%pa might be equivalent to around 1%pa + 4.95%pa = about

Any comments?

I did say "first approximation". I didn't say it would be a good one. It turns out g-1 needs to be more like 120% of f-1, though the actual factor does depend heavily on N.

Fortunately(?) we're not dealing with cases of near-zero interest. :-)

Given a constant monthly payment regime for a fixed number of months, the total amount payable is proportional to the amount borrowed (which in the Halfix case is 2% more than the amount "really" borrowed) and to the interest rate (f-1). It is also inversely proportional to (1-f^-N), and my "first approximation" (foolishly) assumed that if f-1 and g-1 differed only by very little, then 1-f^-N and 1-g^-N would differ insignificantly. That being the case, g-1 and f-1 should differ by the surcharge factor, to break even.

I'm not convinced by your initial/average reasoning. It gets the right result, but I suspect this is purely by chance.

If we're talking about four years (NH):

Borrowing £10200 at 0.4125%pm gives a monthly payment of £234.67. To get the same payment for borrowing £10k, the monthly rate would need to be about 0.49665%; the corresponding "pa" figure is 5.96%.

So if the OP can find a deal at anything less than that (and 5.8% APR

But it does depend on the planned time-profile of the proposed borrowing.

"Ronald Raygun" wrote

Tee hee!

"Ronald Raygun" wrote

Oh ye of little faith! It's not chance at all...

"Ronald Raygun" wrote

That sounds more correct than 5.049% !!

"Ronald Raygun" wrote

Now agreed. [Different to your original conclusion.]

"Ronald Raygun" wrote

Agreed.

For instance, paying off just the minimum amount each month for 47 months, and then whatever is left in month 48 (so that the average balance is higher than with uniform payments), would probably mean that the Halifax deal (2% plus 4.95%pa) is closer to being charged 5.5%pa (the average balance being closer to the inital balance).

Do you agree?...

Actually, it wouldn't have been a bad approximation had the loan been interest-only over a really long term.

More or less, but it's not as simple as that.

You're saying that you can divide the 2% surcharge by the number of years of the term, and then divide the result (0.5%pa in the case of 4 years) by the average/initial balance ratio (which in the case of uniform repayment schedule is 0.5, therefore arriving at an equivalent of 1%pa being added to the rate).

You illustrate this by your latest example showing an ave/init ratio nearer

Yet, consider what would happen if the starting interest rate were not 5%pa but 25%pa. Here, I calculate the top-up equivalent rate to be about 1.2%, despite the fact that (as we know) a higher-rate constant-monthly-payment plan involves an ave/init balance ratio significantly greater than 0.5. I haven't worked it out, but supposing this ratio to be about 0.6, then by your method you'd still start with the 2%, divide by 4 years, getting

You should expect the interest rate to make a difference, because it affects the discounted cash flow, and NPV of all the payments, in a non-linear way. That's what it boyles down to.