The U$.$S$.$A$.$ purchases $$1$ billion of $30-$year bonds from a foreign nation. The bonds yield $4\mathrm{.}5\%$ interest per year. However, there are no annual interest payments made on the bond $($i$.$e$.,$ this is a "zero$-$coupon" bond$).$ Instead, all interest is at the end of the bond life, along with repayment of the face value.

A U$.$S$.$ senator objected to this purchase, saying the correct interest rate for bonds like should be $7\mathrm{.}25\%.$ Assuming the senator$\text{'}$s rate is correct, how much will the foreign country have avoided paying in interest? Express your answer in billions of dollars to $3$ decimal places $(4$ significant figures$).$