371.85=100(1.x) to the 10th power

Question

What is the comopund rate needed to increase $100 to $371.85 over 10 years?

Answer 1

Growth=371.85/100=3.7185=(1+x)¹⁰, so we need the 10th root of 3.7185.

Take logs of each side 10log(1+x)=log(3.7185), log(1+x)=log(3.7185)/10=0.05704 approx (base 10).

1+x=10⁰⋅⁰⁵⁷⁰⁴=1.14035, so x=0.14035 or 14.04% approx.