$(10$ points$)$ A US investor has $$2400$ to invest and can choose either a US investment paying $7\%$ or a foreign investment paying $8\mathrm{.}2\%,$ where e is currently $1\mathrm{.}4.$ What value of e$,$ one year in the future, would leave the investor indifferent between investing at home or abroad? Use $3$ decimals.