Where
- A = payment Amount per period
- P = initial Principal (loan amount)
- r = interest rate per period
- n = total number of payments or periods
How can I rearrange the formula to solve for n?
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Have you tried logarithms? – SK19 Apr 13 '19 at 06:26
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$$A = P \frac{r(1+r)^n}{(1+r)^n -1} \Rightarrow$$
$$A [(1+r)^n -1]= rP (1+r)^n \Rightarrow$$
$$(A-rP)(1+r)^n = A \Rightarrow$$
$$(1+r)^n = \frac{A}{A-rP}\Rightarrow$$
$$n = \log_{1+r} (\frac{A}{A-rP})$$
dcolazin
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Thank you that is working great. I'm using this for a personal budget so that's all I need and I'm able to implement this now. However I don't completely understand how you got from step 2 to step 3 and I am curious. If possible could you elaborate on this? – Caleb Macdonald Black Apr 13 '19 at 07:11
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@CalebMacdonaldBlack Step1: multiply left and right by $(1+r)^n -1$; step2: bring things from the right to the left and then bring the $-A$ to the right; step3: divide left and right by $A-rP$; step4: take the logarithm on left and right; where do you want an explanation? – dcolazin Apr 13 '19 at 07:15