Question

Today the current EUR to USD exchange rate is 1 EURO = 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.

a. Is the USD forecasted to appreciate or depreciate relative to EUR?

i. Appreciate
ii. Depreciate
iii. Neither appreciate nor depreciate
iv. Both appreciate and depreciate

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

A)

USD will depreciate in future by :

Value of $ today = 1∈/1.19$= 0.84033

Value After 4 years = 1∈/1.31$ = 0.76335

B)

Value Of $100 in ∈ Today = 0.84033*100 = 84.033

C)

Value Of Investment after 4 years = P=123.032

Compounding Formula = P=S(1+i)^4

P= 84.033(1+10%)^4

P=123.032

D)

Value of ∈123.032 in USD = 123.032*1.31 = $161.171

E)

Total Return = (161.171-100) = 61.171

Return In % = 61.171/100*100 = 61%

F)

Average Annual Return = Total Return / No of Years

Average Annual Return = 61%/4 = 15.25%

Answer 2

(a) ii Depreciate

(b) 84.03 Euro

(c) 123.03 Euro

(d) 161.17 USD

(e) 61.17%

(f) 15.29%

Step-by-step explanation:

(a) The value of USD is depreciating as you can exchange 1.19 USD for 1 Euro but in after four years, you will need 1.31 USD to exchange for 1 Euro. Thus, you will need more dollars for 1 Euro.

(b) To convert USD to Euro, we just divide the USD with the exchange rate,

Euro = 100 / 1.19 ⇒ 84.0336 Euro

(c) We simply use the compound interest rate formula to calculate the value of our investment after four years with compounding interest,

The formula for compound interest rate is,

A = P(1 + r/n)^nt

Where,

A = Final amount of investment

P = Initial principal Invested

r = interest rate

n = number of times interest is compounded per time period

t = number of time periods

• A = 84.03 ( 1 + 0.1/1)^4 ⇒ 123.028323 Euro

(d) We convert the euros back to USD using the after 4 year exchange rate of 1 Euro to 1.31 USD,

• 123.03 * 1.31 ⇒ 161.17 USD

(e) Total Return in USD = (161.17 - 100) / 100 ⇒ 0.6117 or 61.17 %

(f) The annual average return can be calculated by dividing the total return by the number of years = 61.17% / 4 = 15.2925 %