POP Inc wants to raise $$100,000$ by issuing $20-$year bonds. It may issue bonds $($face value of $$1\mathrm{.}000$ each and paying semi$-$annual coupons$)$ with either $10\%$ or $15\%$ coupon rate. Assume the yield to maturity is $12\%$ no matter which coupon rate POP chooses. Calculate the prices for both bonds and the number of bonds POP need to issue to the required capital?