Two investment proposals, $C$ and $D,$ have the same first cost of $$5,000.$ The

only receipt received from $C$ is a single amount of $$21,500,8$ years from the

time the investment is undertaken. Proposal $D$ has $8$ equal annual receipts of

$$3,000$ beginning one year after the initial investment.

a$.$ Compare $PW(10{)}_C$ with the $PW(10{)}_D.$ Which is larger?

b$.$ Compare $PW(20{)}_C$ with the $PW(20{)}_D.$ Which is larger?

c$.$ On the same axis graph the present worth for each of these proposals as

a function of interest rate. If the present worths are evaluated at the same

interest rate, is there any value of i for which $PW(i{)}_C>PW(i{)}_D?$

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