Question

Today the current EUR to USD exchange rate is 1 EUR = 1.19 USD. According to the Bloomberg consensus estimate, the EUR to USD exchange rate in four years is forecasted to be 1 EUR = 1.31 USD. You begin with 100 USD today and will invest in a European security that provides 10% annual returns (in EUR). Using this information, answer the following six (6) questions.1) Is the USD forecasted to appreciate or depreciate relative to EUR? a) Appreciate b) Depreciate c)Neither appreciate nor depreciate d)Both appreciate and depreciate
2) To invest in the European security you must first convert USD to EUR. How many EUR will you have when exchange your 100 USD today for EUR?

3)Given that you will invest in a European security that earns 10% annually, how many euros will you have in 4 years? Assume that you reinvest all earnings (i.e., your investment simply compounds for 4 years).

4) You live in the US so you wish to exchange EUR for USD after 4 years. How many USD will you have in 4 years after exchanging your euros from the previous problem for USD?

5)What is your total return in USD? Use decimal notation, e.g., enter 0.2345 for 23.45%

6)What is your average annual return in USD? Use decimal notation, e.g., enter 0.2345 for 23.45%. [Hint: You can use your calculators built-in financial function ("fab five") to obtain this answer.]

Answer 1

Answer:

1 . b

2. 84.03 euro

3. 135.28 euros

4. 177.22 dollars

5. 0.77

6. 0.154

Explanation:

1. Dollar depreciated

2. 1 Euro = 1.19 dollars

So therefore

1 dollar = 1 euro/1.19

So 100 dollars = 100 * (1/1.19) = 84.03 Euro.

3. A = p * (1 + (r/n))^(nt)

Where p = principal = 84.03

A = accrued amount after maturity

r = rate = 10%

n = number of compounding = yearly = 1

t = time of maturity = 5

So therefore:

A = 84.03 (1 +0.1)^5

A = 135.28 Euro

4. Convert 135.28 euros to dollars after 5 years

Since 1 Euro = 1.31 dollars

So therefore 135.28Euro will be 1358.28 * 1.31 = 177.22 dollars

5 - (final value/initial value) - 1 )

Where final value = 177.22

Initial value = 100

So therefore [ (177.22/100) - 1] = 0.77

6 - average annual return = sum of earning after maturity / time of maturity

So therefore : 0.77/ 5 = 0.154

Answer 2

Answer:

1) B - The USD is forecasted to depreciate relative to EUR. This is because the value of the USD would go down, more dollar would be required to get 1 EUR worth of goods.

2) Today 1.19 USD = 1 EUR. To get same value of EUR for USD 100

= 100/1.19

= 84.03 EUR

100 USD = 84.03 EUR in today's market

3) Earnings after 4 years in EUR

Current conversion rate:

100 USD in EUR = 84.03 EUR - (from 2 above)

A = P (1 + i)ⁿ

where A = final amount

P = principal invested

r = interest per year

n = number of years invested

∴ A = 84.03 (1 + 0.1)⁴

      = 84.03 * 1.4641‬

      = 123.03‬ EUR

4) Converting from EUR to USD after 4 years

         1 EUR = 1.31 USD

123.03 EUR = 123.03 * 1.31 USD

123.03 EUR = 161.17 USD

5) Calculating return on the investment in USD

ROI = (Gains from the investment - cost of the investment)/cost of the investment

      = (161.17 - 100)/100

      = 61.17/100

      = 0.6117‬

6) Average annual return = [(Ending Value/Beginning Value)$1/n$] -1

                                          = { (161.17/100)$1/4$} - 1

                                          = 1.1267 - 1

                                          = 0.1267

Explanation: