Question

A 1000 par value 5-year bond with 8.0% semiannual coupons was bought to yield 7.5% convertible semiannually. Determine the amount of premium amortized in the 6th coupon payment.

Answer 1

The amount of premium amortized in the 6th coupon payment of the bond is $2.50.

Step-by-step explanation:

The amount of premium amortized in the 6th coupon payment of the bond can be calculated by subtracting the coupon rate from the yield on the bond.

First, let's calculate the coupon payment for each semiannual period. Since the par value of the bond is $1000 and the coupon rate is 8%, the coupon payment for each period will be $1000 x 8%/2 = $40.

The yield on the bond is given as 7.5% convertible semiannually. To convert this to a semiannual yield, we divide it by 2, resulting in a semiannual yield of 7.5%/2 = 3.75%.

Now, to calculate the premium amortized in the 6th coupon payment, we need to find the difference between the coupon payment and the semiannual yield. In this case, it would be $40 - 3.75% of the par value ($1000) = $40 - $37.50 = $2.50.

Thus, the amount of premium amortized in the 6th coupon payment is $2.50.

Answer 2

$2.08

Step-by-step explanation:

For computing the amount of premium amortized in the 6 coupon payment first we have to need to find out the present value which is shown below:

Given that

NPER = 5 × 2 years

RATE = 7.5 ÷ 2 = 3.75%

PMT = $1,000 × 8% ÷ 2 = $40

Future value = $1,000

The formula is shown below:

= -PV(Rate;NPER;PMT;FV;type)

So, after applying the above formula, the present value is $1,020.53

Now the amount of premium is determined by preparing the amortization schedule i.e to be shown in the attachment

Interest = beginning value × rate