Suppose you borrow $2000 at 5% and you are going to make annual payments of $734.42. How long before you pay off the loan?

Here is my solution

2000 = 734.42(1 1/1.05t) / .05

.136161869 = 1 1/1.05t

1/1.05t = .863838131

1.157624287 = 1.05t

t = ln(1.157624287) / ln(1.05) = 3 years

The only part I don't understand is how we get 1.157624287 from the line above. Would we not just be multiplying .863838131 by 1 to simplify? Where does the 1.157624287 come from?

Thanks,