Understanding simple and compounded interest rates

Many students and practitioners are confused with the difference between simple interest and compound interest. Simple interest does not consider interest on interest while compound interest does. It is a good idea to represent them with a graph. For instance, we borrow $1,000 today for 10 years with an annual interest of 8 percent per year. What are the future values if 8 percent is the simple interest and compounded interest rate? The formula for payment of a simple interest rate is as follows:

The future value for compounded interest is as follows:

Here, PV is the load we borrow today, that is, present value, R is the period rate, and n is the number of periods. Thus, those two future values will be $1,800 and $2,158.93. The following program offers a graphic representation of a principal, simple interest payment, and the future values:

import numpy as np
from matplotlib.pyplot import *
from pylab import *
pv=1000
r=0.08
n=10
t=linspace...