Sam wants to save for his retirement. Starting one year from today, he plans to deposit A$\%$ of his annual salary each year into a retirement account. His salary currently is $$B$ and will increase by $C\%$ per year throughout his career. The stated annual interest rate is D$\%$ with annual compounding. How much money will Sam have for his retirement which begins in E years? Give your answer correct to the nearest whole number.

$($Hint: The first payment in his retirement account is one year from today after his first salary increase$)$

A

$5\mathrm{.}00\%$

B

$

$90,000\mathrm{.}00$

C

$2\mathrm{.}00\%$

D

$6\mathrm{.}00\%$

E

$40$

$8.$ Mr$.$ and Mrs$.$ Nash plan to finance their daughter Gabrielle's college education. Gabrielle just turned $10,$ and will be going to college $8$ years from now. She will graduate in $4$ years. The current annual cost of college is $A and they expect this cost to rise by $B\%$ per year going forward $.$ Keep in mind College tuition is paid at the beginning of each school year. So far Mr$.$ and Mrs$.$ Nash have currently $$C$ in their college saving account. They plan to add an additional $D in each of the next $4$ years then they plan to make $3$ equal annual contributions in the next $3$ years. The annual interest rate over the next few decades will be $E\%.$

a$)$ What is the Present value of Gabrielle's cost of college education.

b$)$ Calculate the additional annual payments made to cover Gabrielle's anticipated tuition costs. Give your answer correct to nearest whole number.

A

B

C

D

E

$

$20,000\mathrm{.}00$

$2\mathrm{.}50\%$

$

$9,000\mathrm{.}00$

$$5,000$

$8\mathrm{.}00\%$

$9.$ Jill won the first prize in a national badminton tournament whereby she will receive $A each year for $B$ years with the first payment being made today. The opportunity cost of capital is $C\%.$

a$)$ Calculate the present value of her prize.

b$)$ Calculate the value of her prize at the start of year $5.$

A $,$

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