FFS the bank makes a profit in every example provided.
Because you have chosen imaginary numbers to produce that result. But however the loan is structured, the bank must get its return or it will decline the business.
As Lumifer pointed out, you are proposing an insurance scheme against default. This is an existing structure, perhaps too much so. In the UK it is called Payment Protection Insurance. The problem with PPI is that it was sold under pressure to people who did not need it. The fallout from that has cost some banks billions, or rather, it has forced them to give back billions they should never have received. to the extent that a whole secondary form of dodgy business has sprung up to assist people in making claims for having been mis-sold these policies.
Because you have chosen imaginary numbers to produce that result. But however the loan is structured, the bank must get its return or it will decline the business.
As Lumifer pointed out, you are proposing an insurance scheme against default. This is an existing structure, perhaps too much so. In the UK it is called Payment Protection Insurance. The problem with PPI is that it was sold under pressure to people who did not need it. The fallout from that has cost some banks billions, or rather, it has forced them to give back billions they should never have received. to the extent that a whole secondary form of dodgy business has sprung up to assist people in making claims for having been mis-sold these policies.