RealNumbers

# Compound interest

The profit that we obtain when we lend our money is called **interest**. This profit is directly proportional to the time that the loan lasts and to the amount that we lent, provided that we decide not to increase the amount with the interest earned. The percentage of profit is called **interest rate**. This is **simple interest** and we can calculate its formula with a compound rule of three:

On the other hand, when we add the interest to the amount, we have

**compound interest**and we need a more complicated formula to calcuate the amount*I*will get after*t*years.• Example 1: A bank offers an interest rate of 4%. What amount will we obtain if we deposit 1000€ for 2 years?

We obtain 1081.60 €

Then, the final amount after

*t*years with*r*% of interest rate is:• Example 2: A bank offers an interest rate of 5%. What amount will we obtain if we deposit 3000€ for 5 years?

We obtain 3828.84 €

**Exercise**: Calculate the amount that we will obtain if we deposit 10.000 € in a bank for 10 years if the interest rate is 2%

Solution: 12.189.94 €

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