Finance about interest and loan:

Q: when the $100 loan is paid off in one lump sum at the end of the year

r=10%

Q: when the $ 100 loan is paid off in 12 equal monthly payments.

r=18.5%

r is the APR

Main: question: I dont understand the logics behind this why if i pay monthly , the APR will be higher, can someone use mathematical method to show me the step and conception?

it is better to give a real example