How to get n from EMI = P(r(1+r)^n)/((1+r)^n - 1)

Question

As per subject line

Answer 1

I am going to abbreviate EMI by E and (1+r) by R

 

E = PrRⁿ/(Rⁿ - 1)

 

E/Pr = Rⁿ/(Rⁿ - 1)

 

(E/Pr) - 1 = [Rⁿ/Rⁿ - 1) - 1

 

(E - Pr)/Pr = 1/(Rⁿ - 1)

 

Pr/(E - Pr) = Rⁿ - 1

 

[Pr/(E - Pr) + 1 = Rⁿ

 

E/(E - Pr) = Rⁿ

 

now pass to logarithms on each side and you will have n by a simple division.

 

Please check my algebra very carefully...but I think this is correct!