Two years ago, you took a $10-$year fully amortizing, fixed rate mortgage for $$100,000$ at $7\mathrm{.}5\%$ p$.$a$.$ compounded monthly.

Today, you pay a fee of $$5543$ to refinance into a new mortgage with maturity in $8$ years and interest rate $5\%$ p$.$a$.$ compounded monthly.

Suppose that you hold the maturity to maturity. The IRR of your refinancing equals $\_\_\_\%$ p$.$a$.$ compounded monthly.