Questions: A company issued 7%, 5-year bonds with a par value of 100,000. The market rate when the bonds were issued was 7.5%. The company received 97,948 cash for the bonds. Using the effective interest method, compute the amount of interest expense for the second semiannual interest period (round to 2 decimals). Multiple Choice 3,679.54. 7,346.03 7,000.00 3,500.00 3,673.01.

Solution Steps

To solve this problem, we need to use the effective interest method to compute the interest expense for the second semiannual interest period. Here are the high-level steps:

1. Calculate the semiannual market interest rate.
2. Compute the initial carrying amount of the bond.
3. Calculate the interest expense for the first semiannual period.
4. Determine the carrying amount of the bond after the first interest period.
5. Calculate the interest expense for the second semiannual period using the updated carrying amount.

The semiannual market interest rate is calculated by dividing the annual market rate by 2: \[ \text{semiannual\_market\_rate} = \frac{0.075}{2} = 0.0375 \]

The semiannual coupon rate is calculated by dividing the annual coupon rate by 2: \[ \text{semiannual\_coupon\_rate} = \frac{0.07}{2} = 0.035 \]

The interest expense for the first semiannual period is calculated by multiplying the initial cash received by the semiannual market rate: \[ \text{first\_interest\_expense} = 97948 \times 0.0375 = 3673.05 \]

The carrying amount after the first interest period is calculated by adding the first interest expense to the initial cash received and then subtracting the semiannual coupon payment: \[ \text{first\_carrying\_amount} = 97948 + 3673.05 - (100000 \times 0.035) = 98121.05 \]

The interest expense for the second semiannual period is calculated by multiplying the first carrying amount by the semiannual market rate: \[ \text{second\_interest\_expense} = 98121.05 \times 0.0375 = 3679.54 \]

Final Answer