Final answer:
The question involves calculating the future value of a $10,000 investment over 20 years with a 5% annual interest rate using the compound interest formula. MATLAB code is provided to perform the calculation and plot the investment's growth over time.
Step-by-step explanation:
The question asks for the future value of an investment made 20 years ago with an annual interest rate of 5%. To calculate this, we can use the compound interest formula, A = P(1 + r/n)^(nt), where P is the principal amount, r is the annual interest rate, n is the number of times interest is compounded per year, t is the number of years, and A is the amount of money accumulated after n years, including interest. Since no additional contributions were mentioned, the formula simplifies to A = P(1 + r)^t because the interest is compounded annually (n=1). Here is the MATLAB code to calculate and plot the growth of the investment:
% MATLAB code
P = 10000; % initial investment
r = 0.05; % annual interest rate
t = 20; % number of years
A = P * (1 + r)^t; % future value of the investment
years = 0:t;
values = P * (1 + r).^years;
plot(years, values);
xlabel('Years');
ylabel('Account Value');
title('Growth of a $10,000 Investment over 20 Years at 5% Interest');
The calculated future value, as well as the growth over time, will be displayed through the plot generated by this code.