Sample Practice Problem
ID: #ASD4T
A bond with face amount \(5,000\), redeemable at par, pays coupons at \(7.93\%\) per period for \(n = 9\) periods and is bought to yield \(3.47\%\) per period. Calculate the price of the bond.
(A)6698.8626
(B)8931.8168
(C)10048.2939
(D)26795.4504
(E)8020.6235
📖 Worked Solution & Strategy
Formula
A bond price is the present value of coupons and redemption: \(P=Fr\,a_{\overline n|i}+Cv^n\), where \(v=(1+i)^{-1}\).
Why this formula applies
Discount every coupon and the redemption payment at the investor's yield per coupon period. Relative to redemption value, the sign of the premium is determined by comparing the coupon amount per period, Fr, with yield interest on redemption, iC; this reduces to comparing r with i only when C=F.
Substitution and calculation
\(P = Fr\,a_{\overline{n}|} + C v^n = 5000\cdot 0.0793\cdot 7.6182 + 5000\cdot 0.735648 = 6698.8626\). Requested value: \(6698.8626\).
Answer
The answer is 6698.8626, option (A).
Final Answer: Option (A)
Unlock Full Step-by-Step Solution & Practice
Get instant access to this worked derivation plus procedurally generated practice questions for Exam FM.