Sanders Company is planning to finance an expansion of its operations by borrowing $$52,100.$ City Bank has agreed to loan Sanders the funds. Sanders has two repayment options: $(1)$ to issue a note with the principal due in $10$ years and with interest payable annually or $(2)$ to issue a note to repay $$5,210$ of the principal each year along with the annual interest based on the unpaid principal balance. Assume the interest rate is $12$ percent for each option.

Required

a$.$ What amount of interest will Sanders pay in Year $1$ under option $1$ and under option $2?$

b$.$ What amount of interest will Sanders pay in Year $2$ under option $1$ and under option $2?$

c$.$ Which option is less costly in the long run?