Fairfax Cookie just bought $2$ tons of chocolate chips from Chantilly Chocolate. Fairfax Cookie has been offered the $3$ possible payment options described in the table. If the discount rate is $9\mathrm{.}94\%,$ which of the assertions is true?

Option

Terms of payment $($amount and timing$)$

A from Fairfax Cookie to Chantilly Chocolate

A $$9,600\mathrm{.}00$ today

B

$$12,900\mathrm{.}00in2$ years

C

$$14,700\mathrm{.}00in5$ years

Fairfax Cookie should prefer option A more than option B$,$ and Fairfax Cookie should prefer option A more than option C

Fairfax Cookie should prefer option B more than option A$,$ and Fairfax Cookie should prefer option A more than option C

Fairfax Cookie should prefer option B more than option A and Fairfax Cookie should prefer option C more than option A

Fairfax Cookie should prefer option A more than option B and Fairfax Cookie should prefer option C more than option A

QUESTION $2$

What is $x$ if $x$ equals the value of investment A plus the value of investment $B?$ Investment $A$ is expected to pay $$26,700\mathrm{.}00$ in $6$ years from today and has an expected return of $14\mathrm{.}10$ percent per year. Investment B is expected to pay $$37,200\mathrm{.}00$ in $8$ years from today and has an expected return of $8\mathrm{.}69$ percent per year.

$$31,200\mathrm{.}02($plus or minus $3$ dollars$)$

$$26,658\mathrm{.}29($plus or minus $3$ dollars$)$

$$28,295\mathrm{.}07($plus or minus $3$ dollars$)$

$$6,999\mathrm{.}35($plus or minus $3$ dollars$)$

none of the answers are within $$3$ of the correct answer

QUESTION $3$

Five years ago, James invested $$6,150\mathrm{.}00.$ In $1$ year from today, he expects to have $$9,080\mathrm{.}00.$ If James expects to earn the same annual return after $1$ year from today as the annual rate implied from the past and expected values given in the problem, then how much does James expect to have in $4$ years from today?

$$11,032\mathrm{.}94($plus or minus $3$ dollars$)$

$$11,773\mathrm{.}16($plus or minus $3$ dollars$)$

$$11,471\mathrm{.}29($plus or minus $3$ dollars$)$

$$12,400\mathrm{.}94($plus or minus $3$ dollars$)$

none of the answers are within $3$ dollars of the correct answer