$1.$ The interest rate is $8\%$ p$.$a$.$ compounded monthly.

A project requires an investment of $$1000$ today. It pays $$100$ in $35$ days, $$200$ in $64$ days, $$300$ in $100$ days, and $$450$ in $300$ days.

The IRR of this project is $\_\_\_\_\%$ p$.$a$.$ compounded monthly.

$2.$ A project requires an investment of $$1500$ today and generates a payment every $50$ days.

Specifically, it pays $$200$ in $50$ days, $$400$ in $100$ days, $$500$ in $150$ days, $$450$ in $200$ days.

Suppose that you can borrow at $5\%$ p$.$a$.$ compounded annually and reinvest your cash at $6\%$ p$.$a$.$ compounded annually.

The modified IRR of this project is $\_\_\_\_\_\_\%$ per annum, compounded annually.

Note: assume that $1$ year includes $365$ days.