$1)$ Consider a coupon bond that has a par value of $$$$900$ and a coupon rate of $10\%.$ The bond is currently selling for $$$$966\mathrm{.}00$ and has $2$ years to maturity. What is the$$ bond's yield to maturity$($YTM$)?$

The yield to maturity is$?$

$2)$What is the price of a perpetuity that has a coupon of $$$$40$ per year and a yield to maturity of $2\mathrm{.}5\%?$

The price of the perpetuity is $$$$\_\_\_$

$3)$ A bond has a face value of $$$$1000$ and an $8\%$ coupon$$ rate, its current price is $$$$940,$ and it is expected to increase to $$$$960$ next year.

The current yield is $\_\_\_\%$

$4)$ How much would you pay for a perpetual bond that pays an annual coupon of $$$$200$ per year and yields on competing instruments are $10\%?$

You would pay $$\_\_\_\_$