National Debt Lab: Growth, Interest, and Primary Balance
Change illustrative interest, growth, and primary balances to track a debt-to-GDP ratio and its steady-balance condition.
Free, with no sign-up.
For High school students and adults reviewing the topic.
About 10 minutes.
How does it work?
- Change the controls or open a named preset. Read the outputs, then check a challenge.
What will you get?
Compare the model’s outputs and check two challenges.
What does the model assume?
- All figures are illustrative. Rates and the primary balance stay fixed for the chosen period; this is an accounting model, not a forecast.
- The identity is d(t) = [(1 + r) / (1 + g)] × d(t−1) − s. Here d is debt as a percentage of GDP, r and g are nominal rates written as decimals, and s is the primary surplus as a percentage of current-year GDP.
- A positive primary balance is a surplus; a negative value is a deficit. Primary means excluding interest payments.
- Interest applies to the preceding debt stock. GDP grows at the stated nominal rate. There are no valuation changes, debt write-offs, or other stock-flow adjustments.
- Negative ratios represent net financial assets. The same illustrative interest rate applies after the ratio crosses zero; values are not clamped at zero.
- The primary surplus that holds the starting ratio steady is [(r − g) / (1 + g)] × d(0). Annual changes are measured in percentage points.
Which setup would you like to try?
What can you change?
Range: 0 to 200 %.
Range: 0 to 15 %.
Range: -5 to 15 %.
Range: -10 to 10 % of current GDP.
Range: 1 to 30 years.
What does the model predict?
| Quantity | Value | Unit |
|---|---|---|
| Final debt-to-GDP ratio | 66.12 | % |
| Change in the final year | -1.27 | percentage points |
| Primary surplus to hold the starting ratio | -1.5094 | % of current GDP |
The solid line gives the ratio at each year end. The dashed horizontal line marks zero.
| Year | Debt / GDP (%) | Change (percentage points) |
|---|---|---|
| 0 | 80.00 | Starting value |
| 1 | 78.49 | -1.51 |
| 2 | 77.01 | -1.48 |
| 3 | 75.56 | -1.45 |
| 4 | 74.13 | -1.43 |
| 5 | 72.73 | -1.40 |
| 6 | 71.36 | -1.37 |
| 7 | 70.01 | -1.35 |
| 8 | 68.69 | -1.32 |
| 9 | 67.40 | -1.30 |
| 10 | 66.12 | -1.27 |
Can you reach these targets?
At a starting ratio of 60%, interest of 5%, and zero growth, find the primary surplus that keeps the ratio flat for ten years.
- Target: Starting debt-to-GDP ratio = 60 %; tolerance 0 %.
- Target: Nominal interest rate = 5 %; tolerance 0 %.
- Target: Nominal GDP growth rate = 0 %; tolerance 0 %.
- Target: Years = 10 years; tolerance 0 years.
- Target: Final debt-to-GDP ratio = 60 %; tolerance 0.01 %.
- Target: Change in the final year = 0 percentage points; tolerance 0.01 percentage points.
Start at 80%, with interest and growth both 5%. Choose a primary surplus that brings the ratio to 60% after ten years.
- Target: Starting debt-to-GDP ratio = 80 %; tolerance 0 %.
- Target: Nominal interest rate = 5 %; tolerance 0 %.
- Target: Nominal GDP growth rate = 5 %; tolerance 0 %.
- Target: Years = 10 years; tolerance 0 years.
- Target: Final debt-to-GDP ratio = 60 %; tolerance 0.01 %.