Part 1The following data are given:Et = yen¥115115 = $1.00Et+1 = yen¥130130 = $1.00 (one year later)i Subscript Japan = 66% annuallyi Subscript U.S. = 1212% annuallyPart 2Calculate the future value of $1,000 in one year invested in the United States and Japan.Part 3If invested in the United States, the future value is $[input]enter your response here . (Round your response to the nearest penny.)

Question

Part 1The following data are​ given:Et​ = yen¥115115 ​= $1.00Et​+1​ = yen¥130130 ​= $1.00 ​(one year​ later)i Subscript Japan​ = 66​% annuallyi Subscript U.S.​ = 1212​% annuallyPart 2Calculate the future value of​ $1,000 in one year invested in the United States and Japan.Part 3If invested in the United​ States, the future value is ​$[input]enter your response here . ​(Round your response to the nearest penny.​)

BlackTom AI · Accepted Answer

First, let's restate the key data and what is being asked in Part 2 and Part 3 to ensure clarity.
- Current exchange rate: 1 USD = 115 JPY (i.e., Et = ¥115 per $1).
- Future exchange rate (one year later): 1 USD = 130 JPY (Et+1 = ¥130 per $1).
- Japanese annual interest rate: 6% (i_Japan = 6% annually).
- U.S. annual interest rate: 12% (i_US = 12% annually).
- Amount to invest: $1,000.
- Part 2 asks for the future value of $1,000 if invested in the United States and in Japan (two separate scenarios).
- Part 3 asks for the numerical value when invested in the United States, which is $[input].

Now, evaluate the United States investment option step by step.
- Step 1: If you invest $1,000 in the United States at 12% for one year, you simply apply the interest on the principal.
  FV_US = 1000 × (1 + 0.12) = 1000 × 1.12 = 1120.00.
- Step 2: There is no currency conversion needed in this path, since the investment is domestic and uses USD throughout the period.

Next, consider the alternative path (for completeness, though the question in Part 3 only asks for the US path):
- Step 3: If you were to invest in Japan, you would first convert USD to JPY at the current rate: 1000 USD × 115 JPY/USD = 115,000 JPY.
- Step 4: Grow that amount in Japan at 6% for one year: 115,000 × (1 + 0.06) = 121,900 JPY.
- Step 5: Convert back to USD at the future rate: 121,900 JPY ÷ 130 JPY/USD ≈ 938.46 USD (rounded for illustration).

Comparing the two options (for context): the U.S. investment yields 1120.00 USD, while the Japanese investment yields approximately 938 USD when converted back, illustrating how higher U.S. interest coupled with exchange-rate movements can lead to a larger future value in dollars in this scenario.

Therefore, the future value of $1,000 invested in the United States for one year is 1120.00 dollars. The precise value you’d enter for Part 3 is 1,120.00, formatted as required (nearest penny).

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