A company issued 7%,five-year bonds with a par value of $100,000.The market rate when the bonds were issued was 7.5%.The company received $97,947 cash for the bonds.Using the effective interest method,the amount of interest expense for the first semiannual interest period is:
A)$3,750.00
B)$3,673.01
C)$3,705.30
D)$3,428.15
E)$7,346.03

Question

Quizplus · Accepted Answer

To calculate the interest expense using the effective interest method, we need to first calculate the present value of the bond. We can use the following formula to calculate the present value of the bond:

PV = C × (1 − 1/(1 + r)^n)/r + F/(1 + r)^n

where:
PV = Present value of the bond
C = Coupon payment
r = Market interest rate
n = Number of periods
F = Par value of the bond

In this case, the coupon payment is $3,500 (7% of $100,000), the market interest rate is 7.5%, the number of periods is 10 (5 years with semiannual periods) and the par value of the bond is $100,000. Using these values, we can calculate the present value of the bond as follows:

PV = $3,500 × (1 − 1/(1 + 0.075/2)^10)/(0.075/2) + $100,000/(1 + 0.075/2)^10
PV = $97,947

The company received $97,947 cash for the bond, which is equal to the present value of the bond. This means that the bond was issued at par.

For the first semiannual interest period, the interest expense can be calculated as follows:

Interest expense = Beginning carrying value of the bond × Effective interest rate
Beginning carrying value of the bond = Present value of the bond = $97,947
Effective interest rate = Market interest rate for the first semiannual period = 7.5%/2 = 3.75%

Therefore, the interest expense for the first semiannual interest period is:

Interest expense = $97,947 × 3.75% = $3,673.01

The best choice is B because it is the correct calculation of the interest expense for the first semiannual interest period using the effective interest method.

A Company Issued 7%,five-Year Bonds with a Par Value of $100,000.The