It is a very good question. The bank always uses compounding to compute the present value of the loan, which has to equal the borrowed amount. We are going to see more about it in the future, but the bank process is the following:
- Computes the opportunity cost of giving the money to the client. This opportunity cost is the effective rate because the bank could invest in deposits, other loans, reinvest, etc.
- Then, the bank uses that rate to compute the amount per month it needs to charge the client in order to have a present value equal to the amount of the loan (as we did in the mortgage example)
- Finally, the bank computes the APR from the monthly amount.