Suppose we open an account that pays a guaranteed interest rate, compounded annually. You just leave the money and let the compound interest work its magic.
Your account balance will grow in the future and is known as the future value of your starting capital.
To find the VF we have the following formula:
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Where:
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VF: Future value
V: As the initial capital
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i: Interest rate of the compounding period
n: Number of capitalizations
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Let's see it now with an example:
Let's say you want to invest $ 1000 at 5% interest compounded annually. After ten years, the balance would be
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FV = $ 1,000 x (1 + 0.05) ˆ10
which is equivalent to $ 1,628.89.
If the interest is compounded monthly instead of annually, you would get
FV = $ 1,000 x (1 + 0.05 / 12) ˆ120
which is equivalent to 1,647.01.
The difference with compound interest is that simple interest bears interest only on the initial capital. It must be taken into account in each compound interest capitalization, interest is generated from the initial capital plus the interest generated in previous periods.
Simple interest is given by the following formula:
where:
IS: It is the Simple interest
CI: It is the Initial Capital
i: It is the interest rate expressed as a percentage of one, which when multiplied by 100, will be expressed as a percentage.
t: It is the time expressed in years.
If we take into account the previous example we would have:
Is = $ 1,000 x 0.05 x 10 = 500
Therefore, after 10 years, we would have $ 1,500, which is less than the figure that he gave us with compound interest.
