$12.$

Tom got a $30$ year fully amortizing FRM for $$200,000$ at $6\%,$ with constant monthly payments. After $3$ years of payments rates fall and he can get a $27$ year FRM at $5\%,$ but he must pay $2$ points and $$1000$ in closing costs to get the new loan. Think of the refinancing decision as an investment for Tom, he pays a fee now but saves money in the future in the form of lower payments. What is the annualized IRR of refinancing for Tom assuming he prepays the new loan $5$ years after refinancing?

$($Clarification: Tom will prepay the new loan $3+5=8$ years after the house is purchased$)$