$64.$ On the day you retire you have $$1,000,000$ saved. You expect to live another $25$ years

during which time you expect to earn $6\mathrm{.}19\%$ on your savings while inflation averages $2\mathrm{.}5\%$

annually. Assume you want to spend the same amount each year in real terms and die on the

day you spend your last dime. What real amount will you be able to spend each year?

A$.$ $$61,334\mathrm{.}36$

B$.$ $$79,644\mathrm{.}58$

C$.$ $$79,211\mathrm{.}09$

D$.$ $$61,931\mathrm{.}78$

$65.$ Lester's just signed a contract that will provide the firm with annual cash inflows of

$$28,000,$ $$35,000,$ and $$42,000$ over the next three years with the first payment of $$28,000$

occurring one year from today. What is this contract worth today at a discount rate of $7\mathrm{.}25\%?$

A$.$ $$88,311\mathrm{.}08$

B$.$ $$89,423\mathrm{.}91$

C$.$ $$90,580\mathrm{.}55$

D$.$ $$91,341\mathrm{.}41$

$66.$ You are considering the purchase of a home that would require a mortgage of $$150,000.$

How much more in total interest will you pay if you select a $30-$year mortgage at $5\mathrm{.}65\%$ rather

than a $15-$year mortgage at $4\mathrm{.}9\%?($Round the monthly payment amount to $2$ decimal places.

Both interest rates are compounded monthly.$)$

A$.$ $$86,311\mathrm{.}18$

B$.$ $$78,487\mathrm{.}92$

C$.$ $$99,595\mathrm{.}80$

D$.$ $$102,486\mathrm{.}68$

please explain with formulas :$)$