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 $ $0\mathrm{.}185$

Current rand spot exchange rate $ $0\mathrm{.}168$

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 $8\%$

Calculate the following exchange rates $($ZAR and USD refer to the South African rand and U$.$S$.$ dollar, respectively$)$:

a$.$ The current ZAR spot rate in USD that would have been forecast by PPP$.$

Using the IFE, the expected ZAR spot rate in USD one year from now.

b$.$ Using the IFE, the expected ZAR spot rate in USD one year from now.

c$.$ Using PPP$,$ the expected ZAR spot rate in USD four years from now.