What is the annual interest rate?

Question

A deposit of $2200 in a savings account reaches a balance of $2795.63 after 6 years. The interest on the account is compounded monthly. What is the annual intere rate of the account 

Answer 1

2795.63 = 2200(1+r/12)^(6•12)

 

Solve for r.  Steps: divide both sides by 2200 (do not round) giving 

1.270740909 = (1+r/12)⁷²

Take natural logs: ln 1.270740909 = 72•ln(1+r/12)

0.2396001233 = 72 ln(1+r/12)

3.327779491X10^-3 = ln(1+r/12)

1.0033333 = 1+r/12

0.003333323 = r/12

r ≈ 0.04

The rate of interest is 4%