Final answer:
The question deals with bond pricing and requires calculating the present value of cash flows to find the price guaranteeing a minimum yield. Interest rate changes directly affect bond face values, and the calculation is complex, taking account of different redemption scenarios and semiannual interest payments.
Step-by-step explanation:
The subject of this question is related to finance and specifically investment valuation and yield calculation in the field of Mathematics. A student is seeking to understand how to calculate the price that would ensure a minimum yield rate on a bond with particular coupon payments and redemption options. The complexity of the bond's redemption choices requires a thorough understanding of yield rates and bond pricing strategies within financial mathematics, a topic generally covered at the college level.
To find the price that will guarantee an investor a yield rate of at least 12.4 percent, we need to calculate the present value of the bond's cash flows, discounted at the investor's required yield rate. The bond pays semiannual coupons at 3.8 percent, which translates to $38 per half year. The issuer can redeem the bond at the 16th coupon for $2100 or at maturity for $2000. We must compare the present value of the bond's cash flows when redeemed at the 16th coupon and at maturity, both discounted at the yield rate of 12.4 percent convertible semiannually, to determine the maximum price an investor should pay.
Considering the investment valuation, when interest rates rise, bonds previously issued at lower interest rates will sell for less than face value. Conversely, when interest rates fall, those issued at higher interest rates will sell for more than face value.