Peter just invested in a seasoned $1,000 par value with a 6% coupon rate. The bond was originally issued for 25 years and currently has 10 years until it matures. If the market interest is 8% and the bond pays interest semi-annually, then what is he likely to have paid for the bond?

Question

Peter just invested in a seasoned $1,000 par value with a 6% coupon rate.  The bond was originally issued for 25 years and currently has 10 years until it matures.  If the market interest is 8% and the bond pays interest semi-annually, then what is he likely to have paid for the bond?

Quizplus · Accepted Answer

To calculate the current price of the bond, we need to find the present value of its future cash flows, which includes the semi-annual coupon payments ($30 = $1,000 * 6% / 2) and the principal payment ($1,000). Using the formula for present value of an annuity, we get:

PV of coupon payments = $30 / (1 + 4% / 2) + $30 / (1 + 4% / 2)^2 + ... + $30 / (1 + 4% / 2)^20 = $540.36
PV of principal payment = $1,000 / (1 + 4% / 2)^20 = $323.05
Current price of bond = PV of coupon payments + PV of principal payment = $540.36 + $323.05 = $863.41

Therefore, the closest answer choice is C ($864).

Peter Just Invested in a Seasoned $1,000 Par Value with a 6