If you have no idea what is compound interest, you are not going to understand the rest of this article, that or you will be somewhat lost.

Using the concepts of compound interest, how then do you calculate the final amount yielded when you invest a regular amount? And this is rather applicable to us, considering that most of us do not usually invest a lump sum, but rather make a small, regular payment that eventually adds up to something.

Suppose Grandma would like to contribute to your housing fee, $200 monthly, in 10 years’ time, at 5% annual compound. How much will be gotten at the end of it?

Every year, you save $2,400 (12 multiply by $200 monthly)

In the first year, $2,400 multiply 1.05

So in the end, you will yield $30,186. And if you had not invest in it? That’ll be $24,000 instead. So from investing at 5%, you get paid an extra $6,186. Not bad, that is almost one-fourth more of the amount.

The equation can be written as such:

$2,400 ([1.05]^{0 }+ [1.05]^{1}… … [1.05]^{8 }+ [1.05]^{9}) = $30,186

Or if you have a calculator nearby, and I mean those scientific ones like TI-84, you can type this in

$2,400 ∑(1.05)^{n} , where n = 0 to 9.

(∑ is simply just to say sum of all the value of n)

In general, we can express the expression as such:

Regular Payment x ∑(1.0i)^{n}, (∑ is simply sum of all)

Where i is the interest rate, n is the number of period that the interest compounds. Using that, let’s solve the next problem.

Greg wants to save $200,000 at the end of 5 years. He is certain about getting an 8% annual compound. How much then, must he save to reach his goals of $200,000?

Using that formula directly is not going to work, so let’s rewrite the equation

Payment x ∑(1.08)^{5 }**= **$200,000

Payment = $200,000 / ∑(1.08)^{5}

Payment = $200,000 / 7.335

Yearly payment =$27,263 or in another words, he would need to save $2,271 every month. There you go, solving how much to save for each month if you do plan to compound it.

## I Don't Have A Calculator

Of course, you may ask, what if I do not have a scientific calculator. Well, there are several online calculators that can help you with all these calculation of interest.

Then why would I want you to do all these? Several reasons:

- You do not get Internet connection all the time. Imagine the hassle of having to boot up your computer just to find out how much to save.
- You do not need to search for online calculator; they are sometimes designed so that you will be frightened you into investing with them.
- You get a better perspective on what to expect. E.g. How much to save monthly, as opposed to a lump sum yearly.

## Comments

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