Solving the TVM equation for the interest rate

[Gamo]

The HP-55 Mathematics Programs book got two type of TVM program to find the Interest rate.

Direct Reduction Loan: Interest Rate on page: 48

Sinking Fund: Interest Rate on page: 60

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Sinking Fund Interest Rate program also provided the Suggested Guess routines.

This doesn't provide the formula used in this program but I traced the suggested guess
routine and got the formula.

Suggested Guess Formula:

[((FV/PMT) - n) x 2] ÷ [(n - 1)^2 + (FV/PMT)]

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Example:

$40,000 to be accumulated in 11 years; annual payments of $2,564

The interest rate needed is approximately _____ %.

Using the Suggested Guest routine i = 0.0796

Answer: Interest Rate = 0.0678 or 6.78%

Remark:
HP-11C took about 20 seconds
HP-12C took about the same time as 11C so
I'm wondering that the 12C might use this suggested guess routine.


Gamo 2/2020