Problem $15-8$ Valuing Callable Bonds

Assets, Incorporated, plans to issue $$6$ million of bonds with a coupon rate of $7\mathrm{.}9$ percent, a par value of $$1,000,$ semiannual coupons, and $30$ years to maturity. The current market interest rate on these bonds is $7\mathrm{.}4$ percent. In one year, the interest rate on the bonds will be either $8$ percent or $5$ percent with equal probability. Assume investors are risk$-$neutral.

a$.$ If the bonds are noncallable, what is the price of the bonds today? $($Do not round intermediate calculations and round your answer to $2$ decimal places, e$.$g$.,32\mathrm{.}16.)$