Question

A quarterly coupon bond has a face value of $1,000 and a coupon rate of 3.8%. Time to maturity is 21 years and the current yield to maturity is 2.8%. How much is this bond worth? Round to the nearest cent.

Answer 1

To calculate the value of the bond, you need to calculate the present value of the coupon payments and the face value.

Step-by-step explanation:

To calculate the value of the bond, we need to calculate the present value of the coupon payments and the face value, and then sum them up.

The coupon payment is $1,000 * 3.8% / 4 = $9.50 per quarter.

The bond is a quarterly coupon bond, so there will be 4 * 21 = 84 coupon payments in total.

Using the formula for the present value of an ordinary annuity, the present value of the coupon payments is:

Present Value of Coupon Payments = $9.50 * [1 - (1 + 2.8%)^(-84)] / (2.8%)

The present value of the face value can be calculated using the formula:

Present Value of Face Value = $1,000 / (1 + 2.8%)^84

Finally, the value of the bond is the sum of the present value of the coupon payments and the present value of the face value:

Bond Value = Present Value of Coupon Payments + Present Value of Face Value

Calculating these values will give you the worth of the bond.