Lesson: Compound interest
A compound interest means that a yield on the original investment and most of previous interest which were made previously on the investment. Basically, if you spend $1000 for a 10% interest after one period, you have $ 1 100 in the end of the period. But if you're offered a compound interest of 10% for several periods it means that on the $ 1 100 since this amount contains the previously earned interest the interest rate is not calculated but at the next phase.

1. Finite number of compounds
for virtually any individual on this forum it is important to recognize one of the simplest relationships there's on economics. You know that in the event you invest X for a interest rate of R, then your investment will be worth A after N periods. This is given by the mathematical relationship:

X(1 R)^N = A.

R is the percentage factor of this interest rate. E.g. 5% is called 5/100 = 0.05.

This basic equations allows us easily solve for missing values, given that we've got values for the other factors:

X = A / [(1 R)^N]
R = Nth_Root(A/X) - 1
N = log(A/X)/[log(1 R)]
A = X(1 R)^N


Example 1:
Say you can get a 1% yearly compounding interest to a managed forex account for a year and you'd love to have 10 000 available to be credited in the conclusion of the twelve months. You are wondering how much you'd need to deposit now. Well, then we need to fix the equation above for X:

X = A / [(1 R)^N] = 10 000 / (1.01^12) = 8 874.49

This means you would need to deposit $ 8 874.49 for them to become 10 000 in 1 year's time. You may confirm this by inserting the values.


Example two:
You want to spend $ 1 000 at a forex account and you would like it to have increased 50 percent in 15 months' time. What require?

R = Nth_Root(A/X) - 1 = 15th_Root(1500/1000) - 1 ~=2.74% monthly interest

Example 3: Debunking HYIP promises
I made $50 000 the first week, After two months I quit my day job, I made $ 1 402 312 the first year, This system generates 5% weekly on autopilot. These are typical phrases you'll find on sales letters which try to convince you in buying their forex robot (EA) or other HYIP (High Yield Investment Products). You can easily use also the formula provided above to make up your thoughts and some reasoning.

Assume some sales letter is offering you a 5% weekly compounded interest and that it is trying to provide the impression that this could be sustained. You have dollar you are thinking about investing in that project. According to http://www.forbes.com/lists/2010/10/...ires_Rank.html the richest persons on the planet are Carlos Slim Helu and his family with a net worth of USD 53.5 BN dollars. $53.5 billion - ill, eh? Well, let's find out how long you would need to be spent with this product starting with $1 in order to achieve the same quantity of riches (in nominal terms).

N = log(A/X)/ / [log(1 R)] = log(53 500 000 000 / 1)/ / [log(1.05)] = 506 weeks = almost 10 years.

Thus, according to this sales letter, with a $1 investment that you can be equally wealthy as Carlos Slim Helu and his family are currently (in nominal terms) in 10 years!

Of course, there are other concerns. As your account to quantities, your broker cannot offer you similarly geared positions anymore before. It is a suitable tool to debunk claims. Many sales letters have been written on the assumption that the reader doesn't know enough about compounded interest rates to have an intuition about the validity of their claims.


2. Continuously compound interest
To get a continuously compounded investment X with interest rate R over N periods, you can calculate the relationship using Euler's number e:

X * e^(R*N) = A

The factors are calculated such as:
X = A*e^(-R*N)
R = ln(A/X) / N
N = ln(A/X) / R
A = X * e^(R*N)