Tim buys an apartment that costs $$750,000$ with an $85\%$ LTV mortgage. Tim got a $30$ year, $3/1$ ARM with an initial teaser rate of $3\mathrm{.}75\%$ and monthly payments. The reset margin on the loan is $300$ basis points above $1$ year CMT$.$ The index was $1\%$ at the time of origination. Tim also had to pay $3$ points for this loan. Suppose the index rate will remain $1\%$ for the life of the loan and Tim prepays the mortgage in $5$ years. Compute the true APR for this loan. $($Write the answer as a percent so for example $2\mathrm{.}5\%$ should be written as $2\mathrm{.}5,$ not as $0\mathrm{.}025.)$