You are considering the purchase of a brand new Mercedes car but are worried about the maintenance cost of this car relative to other cars. You plan to keep the car for $7$ years and have done some online research that seems to indicate that the cost of maintain the car will be $$500$ in the first year and increase on average by $5\mathrm{.}8\%$ per year. If you wanted to have a fund that would cover the maintenance costs, how much money will you need to deposit in the fund today to cover the maintenance costs for the next $7$ years. Assume your fund earns $8\mathrm{.}1\%$ interest.