You need to borrow $$1000.$ Bank A will lend you the money at $5\%$ interest, compounded annually, whereas Bank $B$ will lend you the money at $5\%$ interest, compounded monthly. Bank $B$ also offers you a free cell phone, valued at $$100,$ if you do business with them. What is the closest answer to the longest duration of the loan for which Bank B would be a etter choice?

a$.10$ years

b$.15$ years

c$.20$ Years

$25$ years