Assume that the U$.$S$.$ one$-$year interest rate is $3\%$ and the one$-$year interest rate on Australian dollars is $6\%.$ The U$.$S$.$ expected annual inflation is $5\%,$ while the Australian inflation is expected to be $7\%.$ You have $$100,000$ to invest for six months and you believe that PPP holds. The spot exchange rate of an Australian dollar is $$0\mathrm{.}789.$ What is the Future Value in USD if you invest in the Australian market and bring the money back to US$?$

a$.101989\mathrm{.}55$

b$.1\mathrm{.}989\%$

c$.4\%.$

d$.407958$