Compute the annual yield $($IRR$)$ for an adjustable rate mortgage $($ARM$)$ of $$150,000,$ with $2$ discount points, initial interest rate of $7\mathrm{.}5\%$ for $30$ years. This ARM has a $1\%$ annual and $3\%$ lifetime interest rate cap. The market interest rates are estimated to be $9\%$ in year $2,10\mathrm{.}5\%$ in year $3,11\mathrm{.}5\%$ in year $4,$ and $13\%$ in year $5.$

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