# Thread: Years left on Loan

1. ## Years left on Loan

I've tried to rearrange the equation below to give an equation in n, to show me the number of years left at a particular interest rate, monthly repayment and loan amount. I am getting lost around taking the n't root.

The following formula is used to calculate the fixed monthly payment (P) required to fully amortize a loan of L dollars over a term of n months at a monthly interest rate of c. [If the quoted rate is 6%, for example, c is .06/12 or .005].

P = L[c(1 + c)^n]/[(1 + c)^n - 1

Any help appreciated, I'd like to see how you got there, about 15 years ago I was not bad at this sort of thing but have maybe lost it a little.

thanks,
Martin.

I've tried to rearrange the equation below to give an equation in n, to show me the number of years left at a particular interest rate, monthly repayment and loan amount. I am getting lost around taking the n't root.

The following formula is used to calculate the fixed monthly payment (P) required to fully amortize a loan of L dollars over a term of n months at a monthly interest rate of c. [If the quoted rate is 6%, for example, c is .06/12 or .005].

P = L[c(1 + c)^n]/[(1 + c)^n - 1

Any help appreciated, I'd like to see how you got there, about 15 years ago I was not bad at this sort of thing but have maybe lost it a little.

thanks,
Martin.
Start by taking the logarithm of both sides.

3. Thanks Mr fantastic,

Done as you said, however and got the following which answers my question.

n = log(A/(A-P*i))/log(1+i)

Thanks,
Martin.