A 2-year coupon bond has a coupon rate of 5% and a face value of $1,000. The current price of the bond is $1,038.75. What is the yield-to-maturity of the bond?

I used this formula

50+(1000-1038.75)/2=30.625

(1000+1038.75)/2=1019.38

30.625/1019.38= .03 or 3%

but this is the approximate solution. how to solve for the exact solution?