I have modified your function to calculate the balance for each year correctly, taking into account the compounded interest, monthly deposits, and the annual government bonus. We will also tabulate the balance for each year and plot the balance over the years.
Here's the updated function:
function lisa_calc(I, M, G, Y)
% I = initial amount put into savings when account opens
% M = monthly amount added
% G = growth rate or interest rate (annual)
% Y = number of years money is saved for
% Convert annual growth rate to monthly growth rate
monthly_interest = (1 + G)^(1/12) - 1;
% Initialize balance array to store balance for each year
balance = zeros(Y+1, 1);
% Set initial balance
balance(1) = I;
% Loop through each year
for year = 1:Y
% Calculate balance at the end of the year with monthly contributions and interest
for month = 1:12
balance(year+1) = balance(year+1) + M; % Add monthly contribution
balance(year+1) = balance(year+1) * (1 + monthly_interest); % Apply monthly interest
end
% Add government bonus at the end of the year
gov_bonus = M * 12 * 0.25;
balance(year+1) = balance(year+1) + gov_bonus;
% Apply annual interest to the entire balance including the initial amount and bonus
balance(year+1) = balance(year+1) + balance(year) * (1 + G) - balance(year);
end
% Plot the balance over the years
figure;
plot(0:Y, balance, '-o');
xlabel('Years');
ylabel('Balance (£)');
title('LISA Account Balance Over Time');
grid on;
% Tabulate the balance for each year
disp('Yearly Balance:');
disp(table((0:Y)', balance, 'VariableNames', {'Year', 'Balance'}));
end
