Answer: $982.48
Step-by-step explanation:
The maximum price you should pay would be the present value of the bond including its cash flows. That is how the price of a bond is computed.
The formula to calculate the price of a bond is;
[tex]Price = Coupon payment * \frac{1 - (1 + yield)^{-n} }{yield} + \frac{Future value}{( 1 + r) ^n}[/tex]
The payments are semi annual so the variables will need to be converted to semi annual variables.
Coupon payment = 9.5% * 1,000 * 1/2
= $47.50
Number of periods = 20 years * 2 = 40 semi annual periods
Yield = 9.7%/2 = 4.85%
[tex]Price = 47.50 * \frac{1 - (1 + 0.0485)^{-40} }{0.0485} + \frac{1,000}{( 1 + 0.0485)^{40} }\\Price = 832.077 * 150.405\\Price = 982.48[/tex]
Price = $982.48
$982.48 should be the maximum price you should pay.
Alternatively, use a financial calculator and input the variables as;
Future Value = $1,000
Payment = $47.50
Number of Periods = 40
Rate = 4.85%
