Compound Interest

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What is Compound Interest?

A compound interest rate is calculated based on both the principal and the accrued interest from previous periods. In other words, compound interest is the interest paid on the interest already received in past periods.

The compound Interest Formula with Annual Interest Payments

Illustration of the compound interest formula with annual interest.

A : Accrued amount (principal + interest)
P : Principal amount (initial deposit or loan amount)
i : annual interest rate
n : number of years

The compound Interest Formula with Intra-Year Interest Payments

Illustration of the compound interest formula with intra-year interest.

A : Accrued amount (principal + interest)
P : Principal amount (initial deposit or loan amount)
i : annual interest rate
n : number of years
t : number of compounding periods per year

Example:

Suppose you invest CHF 100 (principal amount) and receive 10% interest annually. In the end of the year, you will receive CHF 10 in interest and will have an aggregated amount of CHF 110 (accrued amount).  In the second period, if the money is left invested, you will receive again a 10% interest. However, interest is calculated using the new amount (CHF 110) rather than the principal amount (CHF 100). Therefore, you will be compensated with an interest of CHF 11. Every year, the compound interest increases a little bit more, which is also referred to as the compound interest effect. The following two figures illustrate this effect. It is therefore beneficial to begin investing at a young age.

Table showing the increasing compound interest from the example. The compound interest increases from 10 in year 1 to 158 in year 30.

Table Example of Compound Interest www.valueinvestments.ch

Curve representing the growth of compound interest from the example.

Figure Example of Compound Interest www.valueinvestments.ch

The amount of the interest rate is also important. The following table compares the accrued amounts for an initial investment of CHF 100 over 50 years at 5% interest, 10% interest, and 20% interest. The accrued amount for an investment of CHF 100 at a 20 percent interest rate is approximately 77 times higher than at a 10% interest rate in year 50.

Table showing the effect of the interest rate level. The initial investment is CHF 100. After 50 years and an interest rate of 5 percent, the final capital is CHF 1,147. After 50 years and an interest rate of 10 percent, the final capital is CHF 11,739. After 50 years and an interest rate of 20 percent, the final capital is CHF 910,044.

Table Example of Compound Interest: Accrued Amount www.valueinvestments.ch

The following figure compares interest rates of 5%, 10%, and 20% for an initial investment of CHF 100 over a period of 5-10 years. The growth rate appears to be non-linear.

The figure shows the growth of the capital with the different interest rates from the example in a line chart.

Figure Example of Compound Interest: Initial Investment vs. Final Capital www.valueinvestments.ch

Compounding Periods

The number of periods increases the compound interest effect. Consequently, the compound interest increases with the number of compounding periods. The following figure shows the accrued amount for interest over 10 years with an annual interest rate of 10% for three different compounding periods. 

The bar chart shows the difference between the annual, semi-annual and monthly interest rates. With an initial investment of CHF 100, and an interest rate of 10 percent, the final capital after 10 years is CHF 259. With a semi-annual interest rate, the final capital is CHF 265. With a monthly interest rate, the final capital is CHF 270.

Figure Example of Compound Interest: Compounding Periods www.valueinvestments.ch

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