To fund her future MBA program costing $$150,000$ in $7$ years, Emma needs to invest a sum today. What should be her investment at a $3\mathrm{.}5\%$ annual discount rate?

$$

a$.$

$$117,898\mathrm{.}64$

$$

b$.$

$$112,894\mathrm{.}76$

$$

c$.$

$$130,456\mathrm{.}82$

$$

d$.$

$$125,789\mathrm{.}64$

$$

a$.$

$182\mathrm{.}12$ years

$$

b$.$

#NUM $($impossible to solve$)$

$$

c$.$

$48\mathrm{.}75$ years

$$

d$.$

$41\mathrm{.}04$ years