Solving the TVM equation for the interest rate

[Carsen]

Problem #1: n=32 PV=-6,000 FV=10,000 PMT=0 i=???
Answers: 12C=1.609139492% 15C=1.609139501% Prime=1.60913949196%

Problem #2: n=36 PV=13,000 PMT=-372.53 FV=0 i=???
Answers: 12C=0.1692576094% 15C=0.1692569782% Prime=0.169257604168%

Problem #3: n=36 PV=5,750 PMT=-176.89 FV=0 i=???
Answers: 12C=0.56266017270% 15C=0.5626013555% Prime=0.562601726101%

Problem #4: n=360 PV=75,000 PMT=-425.84 FV-0 i=???
Answers: 12C=0.458302324% 15C=0.4583302039% Prime=0.458330232637%

The 12C results is from my 12C bought in 2016. The 15C results is your (Dieter's) program. The Prime's results is using the TVM formula in the 12C manual using your initial estimate formula. Looking at the 15C and the Prime's results, I would say that the estimate works really well. I wonder if there is a even better way to produce a estimate.