A company must pay liabilities of $$300$ in one year, $$500$ in two years and $$600$ in three years. The only investments available are :

$1-$ year zero coupon bonds

$2-$ year $5\%$ annual coupon bonds maturing at par

$3-$ year $7\%$ annual coupon bonds maturing at par

The company purchases a combination of these bonds to exactly match its liablities. How much should the company invest in the $1-$year bond given an annual effective rate of interest of $3\%.$