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?
[Math] How to solve for n (number of periods) in a loan repayment formula
finance
Best Answer
$$A = P \frac{r(1+r)^n}{(1+r)^n -1} \Rightarrow$$
$$A [(1+r)^n -1]= rP (1+r)^n \Rightarrow$$
$$(A-rP)(1+r)^n = A \Rightarrow$$
$$(1+r)^n = \frac{A}{A-rP}\Rightarrow$$
$$n = \log_{1+r} (\frac{A}{A-rP})$$