How to calculate compound interests?

On the contrary of simple interests, compound interests are characterized upon the fact that they calculated upon the obtained amount in the previous period. Take notice of the following difference between applying an amount of 10,000 Euros for four years, upon a rate of 10% a year, according to a Simple Interest regime and according to a Compound Interest regime.

Simple Interests

• Initial amount: 10,000 Euros.
• At the end of the 1st year: 10,000 + 10,000 X 0.1 = 11,000 Euros.
• At the end of the 2nd year: 11,000 + 10,000 X 0.1 = 12,000 Euros.
• At the end of the 3rd year: 12,000 + 10,000 X 0.1 = 13,000 Euros.
• At the end of the 4th year: 13,000 + 10,000 X 0.1 = 14,000 Euros.

Compound Interest

• Initial amount: 10,000 Euros.
• At the end of the 1st year: 10,000 + 10,000 X 0.1 = 11,000 Euros.
• At the end of the 2nd year: 11,000 + 11,000 X 0.1 = 12,100 Euros.
• At the end of the 3rd year: 12,100 + 12,100 X 0.1 = 13,310 Euros.
• At the end of the 4th year: 13,310 + 13,310 X 0.1 = 14,641 Euros.

The difference of a period of four years may seem a short one (only 641 Euros), but if the same amount was applied during 20 years instead of 4 years, at the end of the 20th year, upon a simple interest regime, we would have 30,000 Euros. However, at the end of the same period of time, upon a compound interest regime, the value of our savings would be more than twice and we would have 67,275 Euros. So as to better understand this evolution, pay attention to the following graph:

This difference will be stressed as time goes by, because the growth of the amount upon the type of simple interest gives rise to a linear curve while the value of the amount upon compound interests gives rise to an exponential curve. In order to make this kind of calculation easier, which would last a lot if it was made every year, year after year there are formulas that enable us to calculate the final value after a certain number of years.

Formulas to calculate Interests:

• Simple interest: `C_n = C xx (1 + k xx n)`
• Compound interest: `C_n = C xx (1 + k)^n`

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