$2.$ Imprudential, Inc., has an unfunded pension liability of $$450$ million that must be paid in $20$ years. To assess the value of the firm$$s stock, financial analysts want to discount this liability back to the present. If the relevant discount rate is $5\mathrm{.}2$ percent compounded monthly, what is the present value of this liability?

$3.$At $4\mathrm{.}3$ percent interest compounded quarterly, how long does it take to double your money? To quadruple it$?$

$4.$Consider the following cash flow stream:

t$=0$: $$200$

t$=1$: $$300$

t$=2$: $$300$

t$=3$: $$400$

t$=4$: $$150$

t$=5$: $$250$

If the discount rate is $4\%,$ what is today's value of this stream of cash flows?

$5.$ Suppose that you wish to save $$20,0000$ by making the following deposits:

t$=0$: $$2000$

t$=1$: $$3000$

t$=2$: $$3000$

t$=3$: $$4000$

t$=4$: $$1500$

t$=5$: $$2500$

What must the interest be $($or what is the implied interest rate$)?$