Omni Advisors, an international pension fund manager, uses the concepts of purchasing power parity $($PPP$)$ and the International Fisher Effect $($IFE$)$ to forecast spot exchange rates. Omni gathers the financial information as follows:

Base price level $100$

Current U$.$S$.$ price level $105$

Current South African price level $111$

Base rand spot exchange rate $ $0\mathrm{.}182$

Current rand spot exchange rate $ $0\mathrm{.}165$

Expected annual U$.$S$.$ inflation $7\%$

Expected annual South African inflation $5\%$

Expected U$.$S$.$ one$-$year interest rate $10\%$

Expected South African one$-$year interest rate $8\%$