homeowner can obtain a $$400,000$ thirty year fixed rate mortgage at a rate of $6\%$ with zero points or at a rate of $5\mathrm{.}5\%$ with $2$ points. Assume that the savings in payments can be reinvested at the lower mortgage rate of the two quotes$\mathrm{.}22.$ What is the net present value of paying the points assuming the homeowner holds the loan for $30$ years?A$)$ $$12,812$