Getta Pizza This! is a restaurant that has recently opened. The owner purchased their location with a down payment of $$116,000$ followed by a $25-$year mortgage with equal end$-$of$-$quarter payments of $$5155.$ The interest rate at the time of signing the mortgage papers was $4\mathrm{.}8\%$ compounded semi$-$annually.

a$)$ Determine the purchase price of the restaurant location rounded to the nearest $$1000.(4$ marks$)$

b$)$ Calculate the amount of interest paid from the start of the $15$th year to the end of the $20$th year. Use the rounded value from part $($a$)$ in this calculation. $(7$ marks$)$