Excel gives the value of an infinite series of payments of €13.61 euros at 2.5% interest as having a present value of €498.32. I get the future value of 20 annual payments of €13.61 @ 2.5% as €347.66, which is what I assume they should have owed the NYSE, assuming no interest on today’s payment, or €356.35 if they add one years interest, in other words £288.47 or £295.68. Presumably the bond should have a surrender value of €498.32 or, 1,200 Carolus guilders. I think the numismatic value of the bond, obviously far outweighs any current monetary value.
The value of an infinite series at rate r is equal to PV/r. If the first payment is delayed by a payment period it is PV/(r x (r+1)).
Great analysis. Since inflation obviously has an enormous effect on infinite term debt securities, another useful formula is for the present value of a perpetuity like this one when corrected for inflation. In this case, the present value is equal to the payment divided by the difference between the interest rate and the inflation rate, assuming that the first payment is received at the end of the first period. There are some elegant mathematical derivations of this interesting limit of an annuity.