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Dear all,

I struggle on an approach to solve the following financial calulation:

Given is a saveings plan with a fixed time t[yr], interest rate, static monthly investment and - here comes my issue - an annual bonus which depends on the annual invested money (and so is constant during the whole contract).

I'm now looking on a solution how to calculate the needed interestrate to achive the desired final capital at the end of the contract.
Without this "annual bonus" it is a no-brainer, but with I'm kind of stuck.

Any hints for me?


Pseudo Pascal-ish code for the brute force method...

EXPORT FindInterest(years,monthly,bonus,goal);

LOCAL interest:=0.001;
LOCAL increment:=0.002;
LOCAL i:=0;
LOCAL month:=0;
LOCAL balance:=0;

WHILE balance<goal DO
  FOR i:=1 to years DO
    FOR month:=1 to 12 DO
      balance:=balance+(balance * (interest / 12))+monthly;


RETURN interest;

Now this is going to return the interest at which balance exceeds goal. To get it exact would need additional processing at finer precision.

I’m sure there’s a formulaic way to solve this easier, but it exceeds my math abilities.

Edited to Prime-compliant HP-PPL. Tested on my Prime. It is slow as you’d expect. It could be sped up by providing or calculating a starting guess and larger increment before refining.
Sounds tailor-made for the spreadsheet.

an formularic approach would be exactely what I would be looking for.
I can't believe that this can only be solved by an iterative solution ....
Just use a separate calculation for the bonus compounded annually.

I.e. (compounded value of monthly payments) + (compounded value of bonus)

The reason to suggest the spreadsheet was for generality.
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