How to use yield to maturity to price bond

Question

Hello good people, I please I need your help.

I computed the yield to maturity of a bond with MATLAB, and the answer i had was 0.1556.

The following are the details of the bond:

Maturity date: 10/24/2024

Settlement date: 02/17/2021

Coupon rate: 0.19

Clean price: 109.3056

Coupon frequency: 2

Daycount: Actual/365

YTM obtained: 0.1556

I then decided to discount the coupon payments and the face value with the YTM manually. But the answer I get is different from the bond price above.

I use the formula:

Clean Price = CF1/(1+y/2)^T1 + CF2/(1+y/2)^T2 +CF3/(1+y/2)^T3 +...+CFn-1/(1+y/2)^Tn-1 +CFn/(1+y/2)^Tn

CF1, CF2, ...CFn-1 are semiannual coupon payments

CFn = last semiannual coupon plus face value

CF = 9.5, 9.5, 9.5, 9.5, 9.5, 9.5, 9.5, 109.5

T1, T2,...Tn are years to respective cashflows, and are calculated as: Respective cashflow date - settlement date, all divided by 365

Ti = 0.178082192, 0.679452055, 1.178082192, 1.679452055, 2.178082192, 2.679452055, 3.180821918, 3.682191781

The bond price obtained was 141.9043536. Even when I deduct accrued ineterest of 6.1071, I do not get the original price of 109.3056.

The value I obtain only get a bit closer when I change "y/2" in the formula to just "y".

Please is there something I am not doing right?

How should I apply the YTM to get 109.3056 as the bond price?

Thank you in advance.