$(2.)$ A zero$-$coupon bond promises to pay $$1,000$ in principal $15$ years from now. If interest rate are currently at $5\mathrm{.}00\%$ per year and expected to stay constant over time, at what price does the zero coupon bond trade?

$(3.)$ You have an opportunity to purchase an annuity from an insurance company that offers to pay you $$4,000$ a year for $20$ years. If you want to earn a rate of return of at least $6\mathrm{.}50\%,$ what is the most you are willing to pay today to buy this annuity?

$(4.)$ Cirrus Aircraft estimates the cost of a new factory at $$20\mathrm{.}63$ million and wants it fully funded upfront. Management has decided to save $$1\mathrm{.}1$ million per quarter for this purpose. Assume that the firm can earn $6\mathrm{.}25\%,$ compounded quarterly, on its savings. How many years does the firm have to wait before expanding its operations?

$(5.)$ Determine the internal rate of return for the following sequence of cash flows:

$\backslash$table$[[$Year$,$Cash Flow$],[0,-$$$10,000$

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