Question

you purchase a bond with an invoice price of $1,053 and a par value of $1,000. the bond has a coupon rate of 5.3 percent and there are four months to the next semiannual coupon date. what is the clean price of the bond?

Answer 1

The clean price of the bond is approximately $1,033.21.

Step-by-step explanation:

The clean price of a bond refers to the price of the bond without including any accrued interest. To calculate the clean price, you need to subtract the accrued interest from the invoice price. The accrued interest is the interest that has accumulated between the last coupon payment date and the date of purchase.

In this case, the bond has a coupon rate of 5.3% and there are four months to the next semiannual coupon date. To calculate the accrued interest, you first need to determine the semiannual coupon payment by multiplying the par value of $1,000 by the coupon rate and dividing by 2. In this case, the semiannual coupon payment is $26.50. Next, you need to calculate the daily interest rate by dividing the semiannual coupon payment by 180 (the number of days in a half-year). In this case, the daily interest rate is approximately $0.1472. Multiply the daily interest rate by the number of days from the last coupon payment date to the purchase date to calculate the accrued interest. In this case, the accrued interest is approximately $19.79.

To determine the clean price of the bond, subtract the accrued interest from the invoice price. In this case, the invoice price is $1,053 and the accrued interest is $19.79, so the clean price of the bond is approximately $1,033.21.

Answer 2

To calculate the clean price of the bond, subtract the accrued interest from the invoice price. The clean price is $1,026.5.

Step-by-step explanation:

The clean price of a bond is the price that does not include any accrued interest or any other costs associated with the bond. To calculate the clean price, we need to know the invoice price, par value, coupon rate, and the time remaining to the next semiannual coupon date. In this case, the invoice price is $1,053, the par value is $1,000, the coupon rate is 5.3%, and there are four months to the next semiannual coupon date.

First, let's calculate the accrued interest. The coupon payment is calculated as the coupon rate multiplied by the par value, divided by the number of coupon periods in a year. Since this bond pays coupons semiannually, there are two coupon periods in a year. The coupon payment is therefore ($1,000 * 5.3%) / 2 = $26.5.

To calculate the clean price, subtract the accrued interest from the invoice price. The clean price = invoice price - accrued interest = $1,053 - $26.5 = $1,026.5