Economic Myth Of The Week: Mortgage interest rates are at an all time low

Here's a simpler example of the difference between average and marginal interest rates as they apply to government borrowing.

Let's imagine that three potential first time buyers are each buying a property costing £100,000 (we can ignore likely future falls in capital value here; as people who buy in this market are clearly doing). They have deposits of £40,000; £25,000 and £10,000 respectively and accept mortgage offers as follows:

First buyer: 40% deposit - interest rate 3%
Second buyer: 25% deposit - interest rate 4%
Third buyer: 10% deposit - interest rate 6%

The first buyer clearly pays 3% interest of £1,800 per annum.

The second buyer thinks he's paying 4% on his loan (£75,000 x 4% = £3,000), but actually he's not. He's paying 3% on the first £60,000 of the loan and a marginal interest rate of 8% on the next £15,000. i.e. £60,000 x 3% = £1,800 plus £15,000 x 8% = £1,200; £1,800 + £1,200 = £3,000.

The third buyer thinks he's paying 6% on his loan (£90,000 x 6% = £5,400) but he's not. He's paying a mish-mash of 3% and 8% on the first £75,000 (see second buyer), but the bank is actually charging him a marginal interest rate of 16% on the top slice of £15,000 that needs to bring him up from 75% LTV to 90% LTV, i.e. £75,000 x average 4% = £3,000, £15,000 x 16% = £2,400; £3,000 + £2,400 = £5,400.

That is the fundamental difference between average and marginal interest rates; and it is the marginal interest rates that are important.

So from the banks' point of view, it might still make sense to grant mortgages with 90% LTV; assuming funding costs of 2%, they are making an 14% markup on that last £15,000 of the loan; if banks assume that house prices fall another twenty per cent, they might end up with a loan that is legally secured but unsecured in economic terms, but at least they are making an 14% gross profit of £2,100 per annum. The bank just has to gamble on enough mugs hanging on and continuing to pay the 16% marginal rate for long enough to cancel out all the other loans that go bad and on which there is little or no recovery. Assuming a third of loans go bad in the next five years, that's an average loss of £5,000 (£15,000 x 1/3), but the other two thirds will have earned ther lender an average of £7,000 in extra interest (£15,000 x 14% x 5 years x 2/3).