How to calculate this bond value?

Hey all,
I've got a Question and it's about the Value of a bond. Here is the question:
Company issued a 15 year bond, 3 months ago. This bond pays a semi-annual coupon at a coupon rate of 11% p.a.
The rate of return (discount rate) = 10% p.a.
The Face Value is 100,000$

Question: What is today's price of the bond?

Now I know that since it pays semi annually we have to divide the coupon rate and discount rate by 2.
So we have 5.5% and 5% respectively.
My first instinct was to simply put it into the formula for an Ordinary Annuity and also add the discounted face value at the end:
Price of bond = (5,500 / 0.05)*(1-(1/(1+0.05)^30)) + (100,000 / ((1+0.05)^30))
= 107,686.23

However, this would be the price of the bond if it were emitted today.
Instead, it was emitted 3 months ago, so we have to discount it 3 months less.
So I can get todays value (3 months later) by:
107,686.23 * (1+0.05^0.5) = 110,345.55

(is the ^0.5 correct here? Because the 5% is for half a year, so ^0.5 should make it for a quarter year, aka 3 months)

This is the solution I came up with. However, if I enter the coupon details into the following website:
https://exploringfinance.com/bond-price-calculator/

The result is: 107,629.087
(For Term to maturity I used 14,75 years)
So which is correct? Neither?