Example of Earned Interest Calculation

The interest earned is the amount which results to apply an interest rate in an invested amount. The interest rate is a percentage which is represented by the letter i, and says in what proportion will grow month by month the amount, which has been placed in an investment either in a bank or in another financial institution. To better understand how the quantity is increasing, it will be explained with an example.

Suppose that 20,000 pesos are invested in a bank with an interest rate of 10%, which is expressed as the corresponding decimal: 0.10. After each period, which is usually 1 month, the initial amount will have increased by 10%, according to the general formula:

Cf = Ci * (1 + i)ⁿ

Where:

• Cf = Final capital
• Ci = Initial capital
• i = interest rate in decimal form
• n = exponent that tells the number of periods that have passed

For 20,000 pesos with a 10% rate and after 1 month it remains:

Cf = 20,000 * (1 + 0.10)¹

Cf = 20,000 * (1.10)

Cf = 22,000

Now, if the 20,000 pesos with a 10% rate are maintained for 4 months, it remains:

Cf = 20,000 * (1 + 0.10)⁴

Cf = 20,000 * (1.10)⁴

Cf = 20,000 * (1.4641)

Cf = 29,282 pesos

Also, if the interest rate works monthly but the period is indicated to us in years, it will only be necessary to make the conversion from years to months. For example:

For 20,000 pesos with a monthly rate of 10% for 4 years, it is resolved:

4 years * 12 months = 48 months then n = 48

Cf = 20,000 * (1 + 0.10)⁴⁸

Cf = 20,000 * (1.10)⁴⁸

Cf = 20,000 * (97.0172)

Cf = 1,940,944.68 pesos

1o Examples of calculating interest earned

1.- For 25,000 pesos with a rate of 11% and after 1 month it remains:

Cf = 25,000 * (1 + 0.11)¹

Cf = 25,000 * (1.11)

Cf = 27,750 pesos

2.- For 25,000 pesos with a rate of 8% and after 1 month it remains:

Cf = 25,000 * (1 + 0.08)¹

Cf = 25,000 * (1.08)

Cf = 27,000 pesos

3.- For 32,000 pesos with a 5% rate and after 1 month it remains:

Cf = 32,000 * (1 + 0.05)¹

Cf = 32,000 * (1.05)

Cf = 33,600 pesos

4.- For 10,500 pesos with a 4% rate and after 4 months it remains:

Cf = 10,500 * (1 + 0.04)⁴

Cf = 10,500 * (1.04)⁴

Cf = 10,500 * (1.1698)

Cf = 12,283.51 pesos

5.- For 6,000 pesos with a 15% rate and after 11 months it remains:

Cf = 6,000 * (1 + 0.15)¹¹

Cf = 6,000 * (1.15)¹¹

Cf = 6,000 * (4.6524)

Cf = 27,914.35 pesos

6.- For 15,500 pesos with a rate of 8% and after 7 months it remains:

Cf = 15,500 * (1 + 0.08)⁷

Cf = 15,500 * (1.08)⁷

Cf = 15,500 * (1.7138)

Cf = 26,564.27 pesos

7.- For 5,000 pesos with a rate of 18% and after 26 months it remains:

Cf = 5,000 * (1 + 0.18)²⁶

Cf = 5,000 * (1.18)²⁶

Cf = 5,000 * 73.9489

Cf = 369,744.90 pesos

8.- For 8,500 pesos with a 12% rate and after 4 months it remains:

Cf = 8,500 * (1 + 0.12)⁴

Cf = 8,500 * (1.12)⁴

Cf = 8,500 * (1.5735)

Cf = 13,374.91

9.- For 12,000 pesos with a 6% rate and after 5 months it remains:

Cf = 12,000 * (1 + 0.06)⁵

Cf = 12,000 * (1.06)⁵

Cf = 12,000 * (1.3382)

Cf = 16,058.70 pesos

10.- For 3,000 pesos with a 10% rate and after 15 months it remains:

Cf = 3,000 * (1 + 0.10)¹⁵

Cf = 3,000 * (1.10)¹⁵

Cf = 3,000 * (4.1772)

Cf = 12,531.74 pesos

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