Math Is Fun Forum

Naresh

Member

Registered: 2006-09-29

Posts: 15

Compound interest

Could you all please help me with compound interest .I really do not understand this topic.

fgarb

Member

Registered: 2006-03-03

Posts: 89

Re: Compound interest

Let's start with an example. Say you have $100 in a bank and you will be making a 1% interest rate per year - only added on at the end of every year. How much money will you have in three years?

Well, after one year you will have:

100 * (1.0 + 0.01) = 101 dollars     

After two years you will have:
101 * (1.0 + 0.01) = 100 * (1.0 + 0.01) * (1.0 + 0.01)

And after three years you will have:
100 * (1.0 + 0.01)^3 = $103.03

Does that make sense? If so then let's go to the next step, involving symbols. Let's say instead of getting 1% every year, pertend you get r% interest per year, compounded n times per year. You want to know how much money you make after t years. Then, your compounding will give you

[align=center]

[/align]

Where A-sub-i is the money you start with and A-sub-f is the money you end with. You're multiplying by (1+r/n) each time because you would only get the full r% interest if n was once per year. Now pretend that you wanted the compounding to happen extremely often -- you're always getting some of your interest added back in. This means n is extremely large. There's a formula (which  you can derive with some simple calculus) that

[align=center]

[/align]

If you send n to infinity. So the formula you can use for compounding interest is:
[align=center]

[/align]

Which gets more accurate the larger n is. I think that's how it is anyway, I've never actually had an economics class or anything, so if I have my terminology confused then maybe someone can correct me.