Some might argue that $11 trillion in public debt is not that material for two reasons:
- We don’t have to pay back the principal since we can always refinance; and
- The interest payments are not significant since interest rates are so low.
This suggests a puzzle: assuming that the principal never has to be repaid because of refinancings, and that the interest rates never change, what is the total present value of all the future interest payments?
Make the following assumptions:
- The total debt is exactly $11 trillion.
- All debt securities pay interest at fixed rates. Treat T-Bills and inflation-protected securities as if they make fixed interest payments on fixed principal amounts.
- When any security matures, it is refinanced into an identical security with the same principal and interest rate. The refinancings continue indefinitely.
- The discount rate for each security (and its successors) is the same as its current interest rate.
Oh, and you have five minutes. Please show your work. Good luck!
*This excludes more than $4.7 trillion held by government accounts such as the Social Security trust fund.
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