A 10-year loan of $3,000 is arranged to be settled by payments at the end of each year. It can be repaid under two plan A and B. Plan A simply asks for equal annual payments at an annual effective rate of 5.50%. Plan B is more complex: each year you pay $300 to repay the original loan (ten payments of $300 to repay the $3000); on top of this, at the end of each year the lender charges you r = 6% of the amount of loan outstanding at the start of that year.

Your criterion for choosing a plan is "which has the smaller sum of payments over the ten years?". Which plan do you choose? What value of r would make the plans seem equally attractive to you?