On Reddit historians discussed the oldest debts still being paid:

• The loans that the British took out to fight Napoleon in the early 1800s are still being paid back.
• Debts related to the South Sea Company of the early 1700s – a British public/private partnership given monopoly over trade with South America – continue to be paid.
• But the oldest bonds still being serviced are likely those issued by a Dutch water board entrusted with maintaining the condition of local dykes in 1624, almost 400 years ago.
• The currency that this debt is paid in has changed from Carolus Guilders to Flemish Pounds to Dutch Guilders to Euros, tracing the rise and fall of empires.
• Many of these debts are set up as perpetuities – they will pay interest until the end of time – and so could continue to be paid for a long while yet.
• Usually such debts are taken out when the government can get abnormally low interest rates – for example when citizens buy war bonds in a patriotic fervour.
• In such cases inflation will quickly eat away at the value of the interest that has to be paid, making the debt a great deal for the government.

Find the full discussion here.

Source: Reddit