You are considering saving some money to invest in an apartment in $5$ years from now and so you decide to invest in a bond. You are considering two potential bond investments:

a$)$ A zero$-$coupon bond that will get your desired $10\%$ return, due to mature in $5$ years and a face $($par$)$ value of $400\mathrm{.}000$ JPY$.$ How much would you be willing to pay today based on the given information about the bond? How much will you gain by investing in this bond?

b$)$ A level$-$coupon bond with $250,000JPY$ face $($par$)$ value, maturity date in $5$ years and coupons are paid semi$-$annually at an interest rate of $7\%$ and YTM $($Yield to Maturity$)10\%.$ Which option would you choose?$]$