Calculate Simple Interest and Compound Interest – easy exercises with Matlab

1.- Simple Interest

To help us work and calculate the simple interest, we have these two easy formulas:

I = P r t
A = P + P r t 

where
I = simple interest
P = principal
r = interest rate per year
t = time in years
A = amount
 

Examples

If an individual borrows $1000 at 5% per year for 1.5 years, how much interest must be paid on the loan?

I = P r t
I = 1000 (0.05) (1.5)
I = $75
 

If an organization invests $13000 at 4% per year for 3 years, how much will the investment be worth at the end of the 3 years?

A = P + Prt
A = $13000 + $13000 (0.04) (3)
A = $14560 

2.- Compound Interest

Compound interest means that the interest is paid periodically over the term of the loan which results in a new principal at the end of each interval of time. 

The ending balance is given by: 

where
A = amount, or ending balance
P = principal
r = annual interest rate
n = compounded times per year
t = number of years  

The following video shows an example and a solution using a calculator specially prepared for such purpose. After the video, we show how to solve the problem by creating in Matlab our own function for the task...

Let's create our code! - Example

Find the amount of an investment if $10,000 is invested at 5% compounded monthly for three years. 

Fortunately, we can create a function in Matlab for the compound interest formula, like this: 

function A = comp_int(P, r, n, t)
A = P*(1 + r/n)^(n*t);
 

and we can call it from another m-file, script, or from the command window, in this way: 

P = 10000;
r = 0.05;
n = 12;
t = 3; 

format bank
A = comp_int(P, r, n, t)
 

The answer is: 

A = 11614.72

3.- Continuously Compounded Interest

When the interest is compounded more frequently, we get to a situation of continuously compounded interest. This formula works it out: 

A = Pe^rt

where
A = amount, or ending balance
P = principal
e = 2.718281...
t = number of years
r = annual interest rate
 

Example

Find the amount of an investment if $10000 is invested at 5% compounded continuously for three years. 

Fortunately again, we can create another function to calculate the formula above, like this: 

function A = comp_int_2(P, r, t)
A = P * exp(r*t); 

and we can call it from another script or from the command window, in this way: 

P = 10000
r = 0.05
t = 3
A = comp_int_2(P, r, t)
 

The answer is:

A = 11618.34