Assume you buy a house for $$540,000$ and have $$108,000$ as a down payment. Your mortgage rate is $3$ percent APR compounded semi$-$annually and you amortize the mortgage over $25$ years with monthly payments. You will assume that you could have earned $5$ percent EAR on the down payment $($opportunity cost$),$ your marginal income tax rate is $40$ percent, real estate fees are $4$ percent $+$ HST$,$ and property taxes will be $$5,400$ annually for this calculation. Ignore maintenance costs.

a$.$ What is the true return on your investment if you sell it in $6$ years for $$860,000?($Do not round your intermediate calculations. Round your answer to $2$ decimal places. Omit the $"\%"$ sign in your response.$)$

Return on Investment $1\%$

b$.$ What is an approximate annualized rate of return on your investment? $($Do not round your intermediate calculations. Round your answer to $3$ decimal places. Omit the $"\%"$ sign in your response.$)$

Annualized Rate of Return $\%$