You are considering investing in an international bond that is trading in Euros. You see that the bond has a coupon rate of $5\%,$ a par value of $1,000,$ and $10$ years left to maturity. The bond makes payments $1$ time per year.

a$)$ If the market rate of interest is $6\%,$ what would you be willing to pay for this bond?

b$)$ What would you be willing to pay if it instead made $2$ payments per year?