Answer:
Total Value of the Bond = Present Value of Coupons + Present Value of Face Value
Total Value of the Bond = $11.74 + $86.96
Total Value of the Bond = $98.70
Therefore, the value of the bond is approximately $98.70.
Step-by-step explanation:
The value of a bond can be calculated using the present value formula. The present value of a bond is the sum of the present values of the future cash flows from the bond, which include both the periodic interest payments (coupons) and the final principal payment (face value).
Step 1: Calculate the present value of the periodic coupon payments using the coupon rate and the discount rate.
Coupon Payment = Face Value * Coupon Rate
Coupon Payment = $100 * 13.5% = $13.50
Present Value of Coupons = Coupon Payment / (1 + Discount Rate)^n
(where n is the number of periods until maturity)
Note: Since the bond's coupon rate and the discount rate are the same in this case, the bond is priced at par value.
Present Value of Coupons = $13.50 / (1 + 15%) = $11.74
Step 2: Calculate the present value of the face value payment (final principal payment) at maturity.
Present Value of Face Value = Face Value / (1 + Discount Rate)^n
Assuming this is a typical bond with a single maturity period, the present value of the final principal payment is as follows:
Present Value of Face Value = $100 / (1 + 15%) = $86.96
Step 3: Calculate the total value of the bond by summing the present values of the coupons and the face value.