What is the approximate price of a $10,000 coupon bond that pays $1,000 in one year and $1,000 in two years at maturity? The effective yield on the bond is 6 percent.

Question

Quizplus · Accepted Answer

The present value of each coupon payment can be calculated using the formula:

PV = Coupon Payment / (1 + Yield)^n

where PV is the present value, Yield is the effective yield, Coupon Payment is the amount of the coupon payment, and n is the number of periods until the payment is made.

For the first coupon payment of $1,000, n = 1, so:

PV1 = $1,000 / (1 + 0.06)^1 = $943.40

For the second coupon payment of $1,000, n = 2, so:

PV2 = $1,000 / (1 + 0.06)^2 = $890.00

The present value of the bond is the sum of these two amounts:

PV(Bond) = PV1 + PV2 = $943.40 + $890.00 = $1,833.40

Therefore, the approximate price of the bond is $1,833.40.

Since the face value of the bond is $10,000, we can calculate the percentage price of the bond:

Percentage Price = (Price / Face Value) x 100%

Percentage Price = ($1,833.40 / $10,000) x 100% = 18.33%

Therefore, the choice that is closest to this percentage price is B ($10,730).

What Is the Approximate Price of a $10,000 Coupon Bond