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 says 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 in years, it will only be necessary to convert 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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