Function Version: Determining Effective APY

In case you're more into functions:

function effective_apy_midpoint = effective_APY_midpoint(P,Y,n)

% Determines the effective annual yield (APY) given a principal amount, 

% a final amount, and number of years.

% Need to calculate r (APY)

% Use mid-point algorithm

% Formula is Y = P(1+r)^n

% Assume range of r from 0 to 5 (0 % to 300%)

r_min = 0;

r_max = 5;

current_guess = r_min;

Y_temp = P*(1+current_guess)^n;

num_guesses = 1;

while Y_temp ~= Y

    if (Y_temp > Y*0.9999) && (Y_temp < Y*1.0001)

        break

    end

    if Y_temp < Y

    next_guess = (current_guess + r_max)/2;

    else next_guess = (r_min + current_guess)/2;

    end

    Y_temp = P*(1+next_guess)^n;

    if Y_temp < Y

        r_min = next_guess;

    else r_max = next_guess;

    end

    current_guess = next_guess;

    num_guesses = num_guesses + 1;

    Y_temp = P*(1+current_guess)^n;

end

effective_apy_midpoint = current_guess;