$3)$You are given the following information about Bond X and Bond Y:

i$)$ Both bonds are $20-$year bonds.

ii$)$ Both bonds have face amount $1500.$

iii$)$ Both bonds have an annual nominal yield rate of $7\%$ compounded semiannually.

iv$)$ Bond X has an annual coupon rate of $10\%$ paid semiannually and a redemption value C$.$

v$)$ Bond Y has an annual coupon rate of $8\%$ paid semiannually and a redemption value C$+$K$.$

vi$)$ The price of Bond X exceeds the price of Bond Y by $257\mathrm{.}18.$

Calculate K$.$