The projected trade deficits for a country in 2021-2023 are in the following table:

Year Net Exports (billion $)
2021 -10
2022 -5
2023 0
2024 ?

You are asked to calculate the size of the trade surplus required to balance the sum of net exports for the 2021-2024 period in present discounted value terms (i.e., in 2021 dollars). You know that future values are discounted at rate
𝑖
=
3
%
. The 2024 surplus that accomplishes this goal is $______ billion.

Round your answer to the nearest tenth of a billion.

Question

The projected trade deficits for a country in 2021-2023 are in the following table:

Year	Net Exports (billion $)
2021	-10
2022	-5
2023	0
2024	?

You are asked to calculate the size of the trade surplus required to balance the sum of net exports for the 2021-2024 period in present discounted value terms (i.e., in 2021 dollars). You know that future values are discounted at rate 
𝑖
=
3
%
 . The 2024 surplus that accomplishes this goal is $______ billion.

Round your answer to the nearest tenth of a billion.

BlackTom AI · Accepted Answer

Discount future net exports to 2021 and set their present discounted values (PDV) to sum to zero.

1) Relevant concepts
- Present discounted value: PV of a future amount Y received n years from now is Y/(1 + i)^n.
- Here i = 3% = 0.03. 2021 is the base year (n = 0). 2022 is n = 1, 2023 n = 2, 2024 n = 3.
- We need PDV(2021) + PDV(2022) + PDV(2023) + PDV(2024) = 0 and solve for the 2024 surplus.

2) Step-by-step reasoning and algebra
Let X be the 2024 surplus (in billions). Write PDV terms:
- PV(2021) = -10 (already in 2021 dollars)
- PV(2022) = -5 / (1.03)
- PV(2023) = 0 / (1.03)^2 = 0
- PV(2024) = X / (1.03)^3

Set sum to zero:
-10 + (-5)/(1.03) + 0 + X/(1.03^3) = 0

3) Intermediate calculations
Compute discount factors:
1/(1.03) = 0.970873786
1/(1.03)^3 = 1/(1.092727) = 0.915141659

Compute PV contributions:
PV(2022) = -5 × 0.970873786 = -4.854368932

Plug into equation:
-10 - 4.854368932 + 0.915141659 × X = 0
=> 0.915141659 × X = 14.854368932
=> X = 14.854368932 / 0.915141659 = 16.233... (billion)

Round to nearest tenth: 16.2 billion.

4) Why this is correct
This X exactly offsets the discounted deficits in 2021 and 2022 so that the total present value over 2021–2024 equals zero. All future amounts are discounted back to 2021 consistently using (1 + i)^n with correct n.

5) Other options / common mistakes
- A common error is discounting the 2024 amount by only two years (using (1.03)^2) or not discounting at all. That understates the required nominal surplus in 2024. 
- Another mistake would be forgetting to discount 2022; that also yields the wrong X.

6) Conclusion
The required 2024 trade surplus is 16.2 billion, which matches the provided answer.

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