ThermoTech Systems recently sold a $$20$ million bond issue with a $20-$year

maturity and a coupon rate of $11\%$ compounded semiannually. The bond

indenture contract requires ThermoTech to make equal payments at the end of

every $6$ months into a sinking fund administered by National Trust. The sinking

fund should accumulate the full $$20$ million required to redeem the bonds at their

maturity. Round the sinking fund payments and periodic interest earnings to the

nearest dollar.

a$)$ What must the size of the sinking fund payments be if the fund

earns $8\mathrm{.}5\%$ compounded semiannually?

b$)$ How much interest will the fund earn in the sixth year?

c$)$ How much will the fund increase in the $27$th payment interval?