参考答案：B

解析：

This is a discount bond since the market interest rate exceeds the coupon rate. The initial liability is equal to the proceeds received when the bond was issued. We can find this amount from the following calculation: FV=50000000; N=10; I=3.5; PMT=1500000; CPT→PV= $ 47920848.67. Round to $ 47920849. The interest expense in the first 6-month period is the initial proceeds multiplied by the semiannual market interest rate of 3.5%. We get: $47920849 ×3.5% =$1677230. Since the total coupon payment is $ 50000000×3.0% = $1500000 the closing liability for the first period is change in liability=$1677230-$ 1500000=$ 177230 plus the initial proceeds, or: $47920849+$177230=$ 48098079. The interest expense in the second 6-month period is the opening liability for the period (the closing liability for the first period) multiplied by the semiannual market interest rate of 3.5%. We get: $ 48098079×3.5% =$1683433. Proceeding in the same way as in the first two periods we should find that the interest expense for the third 6-month period is $1689853. Adding up these three interest expenses gives the cumulative interest expense to the end of the third 6-month period. We get: $1677230+$1683433+$1690853=$5050516.

Professor’s Note: The answer can be identified without calculation. Since the market rate was higher than the coupon rate at issuance, the initial liability must be less than face value. Since bonds were issued at a discount, the cumulative interest expense will be greater than the coupon interest (0.03×3×50 million). Only answer B satisfies both requirements.