Question

(3). A bond has a face amount of $1,000 and matures in 10 years. The semiannual interest payment is $42.5. What is the fair market value of the bond to yield a true interest rate of 8%? (16 points)

Answer 1

Price of the bond = PV of cash flows from it

Period	Pariculars	CF	PVF/PVAF@4%	Disc CF
1-20	Coupon	$             42.50	13.5903	$        577.59
20	Maturity value	$       1,000.00	0.4564	$        456.39
Price of the bond	$     1,033.98

CF = Interest i.e., 42.5 (Given)

As semi annual interest is paid , PVAF ia 4% (i.e., 8*6/12)

PV of annuity can also be calculated as follows

PV of Annuity
Particulars	Amount
Cash Flow	$           42.50
Int Rate	4.000%
Periods	20

PV of Annuity = Cash Flow * [ 1 - [(1+r)^-n]] /r

= $ 42.5 * [ 1 - [(1+0.04)^-20]] /0.04

= $ 42.5 * [ 1 - [(1.04)^-20]] /0.04

= $ 42.5 * [ 1 - [0.4564]] /0.04

= $ 42.5 * [0.5436]] /0.04

$                      577.59

Pls do rate, if the answer is correct and comment, if any further assistance is required.