A $$1,500$ bond had a coupon rate of $5\mathrm{.}40\%$ with interest paid semi$-$annually. Andrew purchased this bond when there were $9$ years left to maturity and when the market interest rate was $7\mathrm{.}30\%$ compounded semi$-$annually. He held the bond for $4$ years, then sold it when the market interest rate was $3\mathrm{.}20\%$ compounded semi$-$annually.

Calculate the purchase price of the bond.

a$.$

$$1,314\mathrm{.}36$

b$.$

$$786\mathrm{.}76$

c$.$

$$527\mathrm{.}60$

d$.$

$$1,307\mathrm{.}15$