Can you check the first two questions are correct. This is my second attempt at this assignment. I know the last one is wrong but know where I went wrong in the formula. If my formulas are wrong please advise.

Problem

1.Assuming semi-annual compounding, what is the price of a zero coupon bond that matures in 3 years if the market interest rate is 5.5 percent? Assume par value is $1000.

PV= present value, FV= Face value (par value), i= market interest rate, N= year of maturity

PV= FV_N/ (1+i)^N

= 1000 / (1+0.055)³

=1000 / 1.1742413

= $851.61 / 2 = $425.81

2.Using semi-annual compounding, what is the price of a 5 percent coupon bond with 10 years left to maturity and a market interest rate of 7.2 percent? Assume that interest payments are paid semi-annually and that par value is $1000.

PV= present value of interest payments, F= Face value (par value), r= market interest rate, N= time left to maturity, c= coupon rate on bond,

PV= c * F * 1 - (1+r)^-N+ FV

r(1+ r)^N

= .05* 1000 *1 - (1+.072)^-10+ 1000

.072(1+ .072)¹⁰

= .05*1000*(1-.4989/.072) +(1000/2.0042)

=.05*1000*6.9597+489.9522

=$837.51/2= $418.76

3.Using semi-annual compounding, what is the yield to maturity on a 4.65 percent coupon bond with 18 years left to maturity that is offered for sale at $1,025.95? Assume par value is $1000.

Approximate Yield-to-Maturity % = Annual Interest + (Par Value - Bond Price)/Years till Maturity

(Par Value + Bond Price)/2

= (.0465+(1000-1025.95)/18)/ ((1000+1025.95)/2)

= (.0465+-25.95/18) / (2025.95/2)

=-1.4391/1012.9750

=.0014 * 100

= 1.40%