Question $4$: Suppose that you have won a competition in a national newspaper and you

can choose either to receive a lump sum of $$100,000$ now or a payment of $$20,000$ at the

end of each year for the next $7$ years. Assume that the interest rate r is $7\%$ per annum.

$($a$)(15$ points$)$ What is the present value of the payment of $$20,000$ at the end of each

year for the next $7$ years? $($You may use the formula directly$)$

$($b$)(5$ points$)$ Comparing the present value of the income stream obtained in part $($a$)$

and the lump$-$sum of $$100,000,$ which one should you choose?