There
are non-exponential loans. What is considered the norm in the West would be considered as "usury" in many countries of the world. Especially when interest rates of 20-30% are charged in some cases.
https://en.wikipedia.org/wiki/Usury
Even in today's world, there are loans with extremely low or even nil interest rates. Some institutions have a 'Rent to Own' setup whereby you have rental payments over the course of the loan so that at the end of the loan-period you own the asset.
https://ijarahfinance.com.au/islamic-banks/
