$4.$ You are interested in buying a $$1,000$ par value bond with $20$ years to maturity and a $8\%$ coupon rate that is paid semiannually. How much should you be willing to pay for the bond if the required rate of return $($discount rate$)$ is $10\%?$

$5.$ If a semiannual bond with a face value of $$1,000$ has an $8\%$ annual coupon rate and a $10-$year maturity. The current price of the bond is approximate $$933\mathrm{.}55.$ What$$s the annual yield$-$to$-$maturity on this bond?

$6.$ You want to buy a new car. You can make an initial payment of $$3,500$ and can afford monthly payments of at most $$450.$ If the APR on auto loans is $4\mathrm{.}8\%$ and you finance the purchase over $48$ months, what is the maximum price you can pay for the car?