$1)$

a$)$ How much is $$$$225$ to be received in exactly one year worth to you today if the interest rate is $12\%?$

The value today is $$$$\_\_\_\_$

b$)$ If the interest rate is $10\%,$ what is the present value of a security that pays you $$$$1,150$ next$$ year, $$$$1,220$ the year$$ after, and $$$$1,345$ the year after$$ that?

Present value is $$$$\_\_\_\_$

c$)$ 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 $\_\_\_\_$

d$)$ 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 $$$$\_\_\_\_$

e$)$ A bond has a face value of $$$$1,000$ and an $8\%$ coupon$$ rate, its current price is $$$$940,$ and it is expected to increase to $$$$960$ next year.

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

f$)$ 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 $$$$\_\_\_\_$