Question

You buy a 30-year zero coupon bond with a face value of $1000 and a 4% interest rate, compounded semi-annually. The moment after you buy the bond, the interest rate falls to 3%, compounded semi-annually. What is the percent change in the bond price? Note: the sign is important!

Answer 1

Par/Face value	1000
Annual Coupon rate	0
Annual coupon	0
semi-annual coupon	0
Present Value = Future value/[(1+(r/m))^mt]
r is the interest rate that is 4%.
m is the compounding period that is 2
mt is the time period.
price of the bond = sum of present values of future cash flows
r/2	0.02
mt	1	2	3	4	5	6	7	8	9	10	11	12	13	14	60
future cash flow	0	0	0	0	0	0	0	0	0	0	0	0	0	0	1000
present value	0	0	0	0	0	0	0	0	0	0	0	0	0	0	304.7823
sum of present values	304.78
The price of the bond when the interest rate is 4% is $304.78.
Par/Face value	1000
Annual Coupon rate	0
Annual coupon	0
semi-annual coupon	0
Present Value = Future value/[(1+(r/m))^mt]
r is the interest rate that is 3%.
m is the compounding period that is 2
mt is the time period.
price of the bond = sum of present values of future cash flows
r/2	0.015
mt	1	2	3	4	5	6	7	8	9	10	11	12	13	14	60
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