ABC Bank originated a pool of containing $10$ three$-$year fixed$-$rate mortgages with loan amount of $$100,000$ each. All mortgages in the pool carry a rate of $6\%$ with annual payments. The guarantee and servicing fee is $1\%.$ ABC Bank would like to sell the pool to investors via Mortgage Pass Through $($MPT$)$ security. Suppose that $100,000$ shares will be issued and there are no prepayment and no default for the borrowers.

If market interest rate is $5\mathrm{.}5\%,$ what is the price for each MPT security?

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