I'm struggling to rearrange the amortisation formula of a loan to find the interest rate when the other variables are known.

I.e. rearrange $$A = \frac{i \times P \times (1+i)^n}{(1+i)^n-1}$$

To find $$i = ...$$

A = payment amount per period
i = interest rate (for the period)
P = principal amount of the loan
n = number of periods

I ended up with $$A = (1+i)^n(A-iP)$$ which isn't really any closer! Without the pesky i in the second bracket I was going to try to use logs, but I'm stumped and it seems a tad beyond my current limited abilities.

Is there something I'm missing or is quite difficult to rearrange?


This is a question often asked by by those inexperienced in mathematics. [In fact, maybe you can find it already asked here in this forum.]

Such a formula would be very useful.

But there is no such simple formula. That is the main reason why (in the olden days) there were tables published where you would look up the answer. And nowadays you do it with a computer, perhaps even a hand-held one.

  • $\begingroup$ So, no such formula exists? Sounds strange! Is there a reason (in layman's terms) as to why it is isn't possible? Sure, I can work it out via code which loops through and finds the closest interest rate, but I just thought if there was a formula it would be much more efficient to use. Thanks for the answer! $\endgroup$ – Cheesecake Jan 16 '17 at 16:33
  • $\begingroup$ For a rule of thumb to use making a rough estimate: see the "Rule of 78" tiac.net/~mabaker/rule_of_78.html $\endgroup$ – GEdgar Jan 16 '17 at 21:34

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