Question

ilovebonds issued 10-year bonds a year ago at a coupon rate of 8.2 percent. the coupons are semiannual, the par value is $1,000, and the ytm is 6.5 percent. calculate the current bond price?

Answer 1

To calculate the current bond price, determine the semiannual coupon payment, count the remaining payment periods, discount these payments and the final par value to the present at the semiannual YTM rate, and sum these present values together.

Step-by-step explanation:

How to Calculate the Current Bond Price

The question asks us to calculate the current price of a bond with semiannual coupon payments. The bond was issued one year ago with a 10-year maturity, an 8.2% coupon rate, a $1,000 par value, and now has a YTM of 6.5%. To perform this calculation, we follow these steps:

1. Determine the semiannual coupon payment by dividing the annual coupon rate by two and multiplying by the par value: ($1,000 * 8.2%) / 2 = $41.
2. Since the bond has 9 years left to maturity, there are 18 semiannual payments remaining.
3. Calculate the present value of the semiannual payments by discounting them back at the semiannual YTM rate: ($41 / (1 + 6.5%/2)^(1 to 18)).
4. Add the present value of the semiannual payments to the present value of the par value, which is discounted back at the semiannual YTM rate: ($1,000 / (1 + 6.5%/2)^(18)).
5. Sum the present values to obtain the current bond price.

This involves financial mathematics and time value of money calculations.