An insurance company wants to match liabilities of $5,000$ payable in one year and $10,000$ payable in two years with specific assets. The following assets are currently available:

$1$

One$-$year bond with an annual coupon of $5\mathrm{.}25\%$ at par

Two$-$year bond with annual coupons of $4\mathrm{.}50\%$ at par

Two$-$year par value bond with annual coupons of $6\%$ sold at an annual effective yield rate of $6\mathrm{.}5\%.$

Calculate the smallest amount the company needs to disburse today to purchase assets that will exactly match these liabilities.