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

Current U$.$S$.$ price level

$100$

$105$

$111$

$$0\mathrm{.}192$

$$0\mathrm{.}175$

$7\%$

$5\%$

$10\%$

$8\%$

Current South African price level

Base rand spot exchange rate

current rand spot exchange rate

Expected annual U$.$S$.$ inflation

Expected annual South African inflation

Expected U$.$S$.$ one$-$year interest rate

Expected South African one$-$year interest rate

Required:

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$.$

Note: Do not round intermediate calculations. Round your answer to $4$ decimal places.

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

Note: Do not round intermediate calculations. Round your answer to $4$ decimal places.

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

Note: Do not round intermediate calculations. Round your answer to $4$ decimal places.

ZAR spot rate under PPP

Expected ZAR spot rate

Expected ZAR under PPP