Which of the given statements are true?(A) Coupon rate is the annual…

The correct answer is Option (3) → (A), (C) and (D) only

Let a bond have face value F, coupon rate i per period and n periods, so each coupon is Fi. When the discount rate is also i, the present value is

    \( \displaystyle PV=Fi\cdot\frac{1-(1+i)^{-n}}{i}+F(1+i)^{-n} \)

    \( \displaystyle =F-F(1+i)^{-n}+F(1+i)^{-n} \)

    \( \displaystyle =F \)

So when the discount rate equals the coupon rate, the present value of the bond equals its face value.

Checking the statements

(A) Coupon rate is the annual interest rate paid by the bond issuer to the bond holder. — Correct. It is the fixed yearly interest, as a percentage of the face value, paid to the bondholder.

(B) Bonds can only be issued by government entities. — Incorrect. Companies (corporate bonds) and other institutions also issue bonds.

(C) A sinking fund is a fixed term account. — Correct. It is built by regular deposits over a fixed period to collect a known sum at the end.

(D) If discount rate = coupon rate for a bond, then present value of the bond = face value of the bond. — Correct. With both rates equal to i, PV = F.

Tip: A bond sells at par when the discount rate equals the coupon rate, at a premium when the discount rate is lower, and at a discount when it is higher.