Construct synthetically a zero-coupon bond from coupon bonds

The prices of the following coupon bonds are as follows:

Maturity Coupon Price

1 4.75% 103.675

2 7.5% 111.753

3 9.375% 121.445

4 6.25% 114.130

5 5.50% 112.158

How can I construct synthetically a 3-year zero-coupon bond? Which
coupon bonds would I have to invest in? What are the proportions in
which I will have to hold those coupon bonds in order to replicate the
discount bond?

P.S Calculations I did already are show below.

Assuming that coupons are paid annually, I have calculated the implied
term structure of zero coupon rates (not sure if it's correct)

1-yr.disc : = 1.0369%

2-yr.disc : = 1.5079%

3-yr.disc : = 1.9996%

4-yr.disc : = 2.5716%

5-yr.disc : = 2.9503%

I also computed the yields to maturity of the above coupon bonds.



1-yr.disc : = 1.037%

2-yr.disc : = 1.492%

3-yr.disc : =1.947%

4-yr.disc : =2.495%

5-yr.disc : =2.856%

as well as prices of zero-coupon bonds with maturities of 1 to 5 years



1-yr.disc : 100/(1.010369) = $98.97374

2-yr.disc : 100/(1.015079) = $98.5145

3-yr.disc : 100/(1.019996) = $98.0396

4-yr.disc : 100/(1.025716) = $97.49287

5-yr.disc : 100/(1.029503) = $97.13425