Question

A $1,000 bond with a coupon rate of 5% paid semi-annually has 8 years to maturity and a yield to maturity of 9%. The price of the bond is closest to $________. Input your answer without the $ sign and round your answer to two decimal places.

Answer 1

Price of Bond = Present Value of the Future cash flows discounted at YTM or Yield To maturity.

Semiannual interest rate = 5%/2 = 2.5%

Semiannual interest received = $1000*2.5% = $25

Semiannual YTM = 9%/2 = 4.5% OR 0.045

A	B	C	D= B+C	E		D*E
Time (Semiannual)	Semiannual interest	Maturity Amount	Total Cash flow	Present value discounting [email protected]%		Present value of cash flows(D*E)
1	$25	$0	$25	0.956937799	1/(1.045)^1	$23.92
2	$25	$0	$25	0.9157299512	1/(1.045)^2	$22.89
3	$25	$0	$25	0.8762966041	1/(1.045)^3	$21.91
4	$25	$0	$25	0.8385613436	1/(1.045)^4	$20.96
5	$25	$0	$25	0.8024510465	1/(1.045)^5	$20.06
6	$25	$0	$25	0.7678957383	1/(1.045)^6	$19.20
7	$25	$0	$25	0.7348284577	1/(1.045)^7	$18.37
8	$25	$0	$25	0.703185127	1/(1.045)^8	$17.58
9	$25	$0	$25	0.6729044277	1/(1.045)^9	$16.82
10	$25	$0	$25	0.643927682	1/(1.045)^10	$16.10
11	$25	$0	$25	0.6161987388	1/(1.045)^11	$15.40
12	$25	$0	$25	0.5896638649	1/(1.045)^12	$14.74
13	$25	$0	$25	0.564271641	1/(1.045)^13	$14.11
14	$25	$0	$25	0.5399728622	1/(1.045)^14	$13.50
15	$25	$0	$25	0.5167204423	1/(1.045)^15	$12.92
16	$25	$1,000	$1,025	0.4944693228	1/(1.045)^16	$506.83
					Total	$775.32

The price of the bond is closest to $775.32