Quick check on the arithmetic?

With continuous compounding, 1/2 = (1-2.6%)^n = 0.974^n n = log(1/2) / log(0.974) = 26.3 y

Same answer on a Deci-Lon.

With annual compounding, HP-12c gives 27y

I said 50% not 100% :) At 2.5% in 16 years $100 is $148.45