In 2022, the U.S. is running a trade deficit of $1,000 billion. The expected surplus in 2024 is $100 billion. Assuming the interest rate is a constant
4
%
, calculate the trade balance in 2023 such that the present discounted value of the sum of (expected) trade deficits and surpluses (from 2022 to 2024) is zero.

Use a spreadsheet for your calculations and round your answer to the nearest $ billion.

Note: Enter a trade surplus is a positive number and the trade deficit as a negative number. It is easiest to discount the imbalances in 2023 and 2024 back to 2022 (i.e., calculate the present value in 2022 dollars).

Question

In 2022, the U.S. is running a trade deficit of $1,000 billion. The expected surplus in 2024 is $100 billion. Assuming the interest rate is a constant 
4
%
, calculate the trade balance in 2023 such that the present discounted value of the sum of (expected) trade deficits and surpluses (from 2022 to 2024) is zero.

Use a spreadsheet for your calculations and round your answer to the nearest $ billion.

Note: Enter a trade surplus is a positive number and the trade deficit as a negative number. It is easiest to discount the imbalances in 2023 and 2024 back to 2022 (i.e., calculate the present value in 2022 dollars).

BlackTom AI · Accepted Answer

Present-value condition: -1000 + X/(1.04) + 100/(1.04^2) = 0.

1. Relevant knowledge points and concepts
- Present value (PV) and discounting: a future amount A at date t years ahead has PV = A/(1+r)^t where r is the interest rate.
- Here 2022 is the base year (t=0). The 2023 trade balance is one year ahead, 2024 is two years ahead. The sum of discounted trade balances from 2022–2024 must equal zero.

2. Complete reasoning process (step by step)
- Let X be the 2023 trade balance (positive = surplus, negative = deficit).
- Write the PV-sum equation in 2022 dollars:
  -1000 + X/(1.04) + 100/(1.04^2) = 0
- Solve this equation for X.

3. Calculations with intermediate steps
- Compute discount factors:
  1.04^2 = 1.0816
  PV of 2024 surplus = 100 / 1.0816 = 92.4556213 (billion)
- Substitute into the PV equation:
  -1000 + X/1.04 + 92.4556213 = 0
  X/1.04 = 1000 - 92.4556213 = 907.5443787
  X = 907.5443787 * 1.04 = 943.8461547 (billion)
- Round to nearest $ billion: X ≈ 944 (billion).

4. Why the correct answer is correct
- The computed X ensures the present value of the three-year sequence equals zero: discounting the known 2024 surplus and solving for the unknown 2023 value yields the unique X that offsets the 2022 deficit in PV terms. The algebra and numeric discounting above produce X ≈ 943.85, which rounds to 944 billion.

5. Common incorrect approaches (why they are wrong)
- Ignoring discounting and setting -1000 + X + 100 = 0 gives X = 900; this is wrong because future amounts must be discounted to 2022 dollars.
- Using the wrong sign would give a negative number; here the sign is positive because a 2023 surplus is required to offset the 2022 deficit in PV terms.
- Rounding too early can give slightly different intermediate numbers, but final rounding to the nearest billion yields 944.

6. Conclusion
The trade balance in 2023 must be approximately +944 billion. This matches the provided answer: 944.

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