A central heater furnace will not break down completely within 10 years at the least. It may need repairs once in a while but they usually last between 15 to 20 years if it is a good company heater furnace. Although initially it may cost a lot more to purchase and own the central heater furnace, in the long run, you will be glad that you did purchase it because you wouldn't have to worry about paying monthly to rent the furnace.
Of course you would think that what if the furnace break down in the middle of the winter months, then would you have to find the repair guy to fix it for large fees. The truth is most furnaces have at least 10 years of parts warranty and labour warranty for some company could go up to 5 years. So within this period if your furnace breaks down within the labour warranty period and parts warranty period, you can simply call the company you purchased the heater furnace and they will replace the parts and charge you no fees at all. But if you are past the labour warranty period then you only pay for the labour charges fees and you don't have to pay for the parts charges upto 10 years. Now after 10 years, then you will need to pay the company both the parts and labour charges when they come to fix your heater furnace.
When it comes to renting, people say that if the furnace breaks down then you won't have to worry about paying anything to have it fixed. But did you realized that you have been paying them indirectly through your monthly regular payments? Even when your heater furnace is working fine, you pay them monthly. After 10 years of renting you start to lose money because you would have paid to rent more than if you own it. At this time after 10 years, the rental heater company makes every profit monthly from you, until the time that the heater furnace breaks down and they need to replace it with a new one.