A property is expected to have NOI of $$100,000$ the first year. The NOI is expected to

increase by $3\%$ per year thereafter. The appraised value of the property is current $$1$

million and the lender is willing to make a convertible mortgage $($instead of a

participation loan$)$ that gives the lender the option to convert the mortgage balance into

a $60$ percent equity position at the end of year $10.$ That is$,$ instead of receiving the

payoff of the mortgage, the lender would own $60$ percent of the property. The loan would

be for $$900,000$ with a contract interest rate of $9\%,$ and it would be amortized over $20$

years. Assume that the borrower will default if the property value is less than the loan

balance in year $10.$ Further assume that the appraiser would estimate the value in year

$10$ by dividing the NOI for year $11$ by a $10\%$ capitalization rate.

What is the lender s BTIRR $($in decimals, rounded to $3$ digits$)?$