Final answer:
The question involves calculating the realized yield on a bond sold before maturity with reinvestment of coupons at a rate lower than the coupon rate. It relates to financial mathematics within the Business field and requires understanding of bond pricing and investment returns.
Step-by-step explanation:
The subject of this question is Business, more specifically, it is related to financial mathematics and bond investment calculations. A student must calculate the realized yield on a bond that is sold before maturity and when coupon reinvestment rates differ from the bond's original coupon rate. Here's a comprehensive explanation:
First, the coupon payment for the bond will be 6.85% of the $1,000 face value, amounting to $68.50 annually. Over 8 years, these payments would be reinvested at 4.85%, but we'll need additional information or formulas to calculate the future value of these reinvested coupons. When the bond is sold after 8 years with a yield to maturity of 7.85%, the bond price would be lower than the initial purchase price due to the higher yield to maturity. To calculate the selling price, we would use the present value formula for a bond, which takes into account the remaining coupon payments and the face value discounted at the new yield to maturity. The realized yield would then be the combined return from the reinvested coupons and the capital loss or gain from selling the bond.
The given example, which is not directly related to the question but provides context, explains that if a bond paying an 8% coupon is sold for less than face value when market yields rise to 12%, the investor's yield is found by the formula: Yield = (Total Return = Interest Payments + Capital Gains) / Initial Investment.