$1.$ Prof Proton recently retired. He wants to set aside a lump sum amount that will enable him to buy a new car in $5$ years$$ time. The current cost of the car is R $400000\mathrm{.}00.$ The cost of the car will increase by $7\mathrm{.}5\%$ per annum and the amount that he invests will grow at $8\mathrm{.}5\%$ per annum. The amount that he must invest today to be able to buy the car in $5$ years$$ time, is:

R $394258\mathrm{.}76$

R $381903\mathrm{.}49$

R $418954\mathrm{.}02$

R $409841\mathrm{.}37$

None of the above