Imagine you can invest in an electric vehicle $($EV$)$ charger so you can charge your new Tesla Model X at your home. You predict this will save you an average of $$350$ per year for the first year. However, due to rising electricity costs through your energy provider, you estimate that these savings will decrease through time. If the savings will decrease at a rate of $3\%$ and your personal discount rate is $8\%,$ what is the most you would be willing to spend to purchase and install the charger?

Group of answer choices

$$1897\mathrm{.}12$

Cannot solve this problem

$$3181\mathrm{.}82$

$$2562\mathrm{.}19$