We may be able to reel out the formulars for simple and compound interests, but there is nothing as exciting as being able to visualize them! Learn why Albert Einstein called Compound interest, “one of the most powerful forces of nature”.

link: http://samimath.com/visualising-simple-compound-interests/

I remember my Primary School friend, Kayode who sometimes borrowed some money from me and return it few weeks later with a little 'bonus'. He could borrow N10 and return N15 a week later - extra N5 for the boys!

If I had spent the N10 myself, it wouldn't had earned me extra N5 a week later that's 50% extra. The extra N5 was my gain for not using the money myself. Back then, I didnot know that the extra N5 I gained had an official name - Interest.

Interest has been with us for ages, even before we had money. Our fore-forefathers would lend out a number of seeds to their mates and recieve the same number of seeds after the planting season with some additional produce of the seeds as interest. When money was invented, interest was also invented on money borrowed or saved.

So, interst can be said to be money paid on money borrowed from a lender or saved in a bank. It's the bonus you get for not using your money yourself.

Simple Interest - It's really simple

Simple interest is usually expressed as the percentage of the money borrowed and paid after a period of time. It is a fixed amount over time . If someone borrows N10, 000 and is to pay 50% interest at the end of the year, then:

Interst = 50% * N10, 000 = N5,000

That means he will pay back N15, 000 at the end of the year.

Suppose he wants to keep the borrowed money for 6 years.Then the interest he will pay after six years is:

N5,000 * 6 = N30, 000.

Including the money borrowed, he will pay the amount of N40, 000 after 6 years. Easy to compute? That's why it's simple interest.

The Simple Interst Formula

In the example above, we multiplied the percentage with the amount borrowed with the number of years to get the interest for six years. That is:

Simple Interst, I = pecentage * amount borrowed * number of years.

The amount borrowed is usually called the Principal(P), the number of years is called the Time(T) and the percentage to pay is called the Rate(R). So, we can write:

I = P*R*T.

Since Simple interst is constant over a period of time, it can be represented as:

We started with N10, 000 in blue, each year the blue contributes N5000 (in red) to the total amount. An in each new year, our interest is based on our starting amount(the blue) and not our new amount the previous year( the blue + the red). Drawing a line along the path gives a straight line with an uniform steepness, indicating that interest is a fixed percentage of the starting amount. Each year we earn "P*R", no matter the interest we had earned before.

Compound Interest - Something Better or Worse!

You may wonder why in simple interest we earned the same amount each year. why couldn't we make money also from our interests? That's where compound interest comes in.

In simple interest, our interest after each year was 'inactive' - it was only the original amount (principal) that was working and earning more interests! Good news, in compound interests, our principal first makes interest, then the principal and the first interest both make another interest, then the principal, first and second interest also makes interest and so on....cool? Yea, cool for the lender. Bad for the borrower.In fact, Albert Einstein called it, "one of the most powerful forces of nature".

How it works

In compound interest, after each year, the interest is added to the original amount, principal, to get an higher principal for the next year. Let's take an example, suppose that someone borrows, N10, 000 at 50% interest compound interest for 3years:

In the first year:

Principal = 10,000
50% interest after year 1 = N5,000
Amount after year one: 10,000 + 5,000 = N15,000

In the Second year: The previous amount becomes the principal:

Principal = N15, 000
50% interest after year two: N7, 500
Amount after year two: 15,000 + 7500 = 22, 500

In the third year: The previous amount becomes the principal:

Principal = 22 500
50% interest after year three = 11, 250
Amount after year three: 22,500 + 11, 250 = N33, 750

Whoah! He will pay back N33, 750 after three years compound interest. If it were simple interest, the interest after 3 years would be...

I= 10,000 * 50% * 3 = 15,000.
Amount = 15,000 + 10,000.

..he would have payed back N25,000. The difference, N8, 750, is clear!

Since the principal grows each year in compound interest, compound interest can be represented as:

...Just like virus

A virus is dangerous because when it gets into the body of it's host, it produces new virus cells, this new cells also produce new cells and the process continues. This is what happens in compound interest: Principal produces interest, which also produces interest, which also produces interests....

Compound interest trajectory

Unlike simple interest which has a straight line trajectory, the trajectory of compound interest is a curved one! It's steepness changes each year - indicating changing principals and therefore changing interests each year.

Ok, this is getting too long. In the next post, I will discuss the general formular for compound interest and annuity.

Awesome Math!

Source: http://samimath.com/visualising-simple-compound-interests/

lalasticlala, come and see snake interests ooo

it was very helpful

preponey:
it was very helpful

Thanks dude