$46.$ Daniel is planning to make an investment with his income of $$1,000.$ He has two options. Option $1$: Invest in a security that offers an interest rate of $6\%$ compounded annually, with interest payments made in US dollars. Option $2$: Invest in a project that guarantees an interest rate of $5\mathrm{.}9\%$ compounded monthly, with returns paid in the local currency $($Ghanaian cedi, GHS$).$ The current exchange rate between the US dollar and the Ghanaian cedi is $1$ USD $=15$ GHS$.$ Historical records show that the cedi depreciates at an average rate of $6\%$ annually.

Required:

i$.$ Calculate the Effective Annual Rate $($EAR$)$ for the two investments and show which one yields more returns.

ii$.$ Determine the final amount in USD for each investment option after one year. Use the appropriate formulas for each option and explain your calculations.

iii. Convert the final USD amount from each investment option to GHS using the current exchange rate of $1$ USD $=15$ GHS$.$ Calculate the returns in GHS and compare the two options.

iv$.$ Given the historical annual depreciation rate of the cedi $(6\%),$ calculate the expected exchange rate between USD and GHS after one year. Show your calculations and explain the impact of currency depreciation on investment returns.

v$.$ Convert the final USD amount from each investment option to GHS using the depreciated exchange rate calculated in $($iv$).$ Based on these calculations, which investment option offers a higher return in GHS after accounting for the depreciation of the cedi? Provide a detailed explanation and recommendation for Daniel's investment decision.