A $1,000 bond with a coupon rate of 8% has quarterly coupons and is redeemable after an unspecified number of years at $957. The bond is bought to yield 12% convertible semiannually. If the present value of the redemption amount is $355.40, find the purchase price using the Makeham formula. Then check your answer using another price formula.

Please show steps and use formulas. No Excel please. Thank you.