Ok, so you wanted to get pet insurance for your dog, and knowing how expensive that was, you postponed it for the time being. That was fine. You just avoided paying extra money for something that was nice to have, but not really necessary.
What you might think about doing instead is just putting some money aside, perhaps in a special bank account, to cover unexpected issues. That money will likely earn interest and yet, help you cover care and other things like medicine and food. You won't owe monthly premiums or be forced to pay additional money out for price increases and the like. If you didn't sock that money in such a special account, you would probably have to reach deeper in your pocket to cover unexpected costs. But you wisely anticipated those costs and saved ahead of time.
Life is hard
3 years ago