Solver behaviour on HP Prime, 50g, 39gII, TI Nspire CX CAS, and Casio fx-9860GII

On comparing the differences in behavior of TVM calculations, the solver of HP Prime is the only calculator able to return, without any initial guess input, the approximate value of number of period in a peculiar form of future value finding equation, although with not small of an error of about 13%.

Edit: Added results from 50g and 39gII emulator, they both returned the same result (but not the same as the Prime) without being given any hints.

HP Prime:
penny-prime

HP 50g
penny-hp50g

HP39gII
penny-hp39giipenny-hp39gii2

TI Nspire: penny-nspire2

Casio fx-9860GII:
penny-casio1 penny-casio2

The original problem is from an classic HP calculator manual published in 1982. The problem goes like this (example 2 on page 145): If an employee is paid $0.01 every second, with an interest rate of 11.25% compounded every second, what will she get after a year? In the original document, this problem is used to illustrate the limitations numerical accuracy. Detailed explanation and workarounds can be found in the original document.

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