Interest rates play an integral part of economic functions, from encouraging investment to encouraging saving, It is the mere idea of interest that fuels credit and, in turn, allows our world to finance itself. There are many ways that interest can be calculated. These include compounding interest, simple interest and real rate of return. We will be looking at continuous compounding and how it is calculated, as well as the continuous compounding formula, along with some scenarios where it might prove useful.
Understanding the basics is the best way to learn about continuous compounding and the workings of the continuous compounding formula.
Simple interest, as the name suggests, is simply interest earned on the principal amount, term after term. Simple interest does not add to the principal amount, and the interest is paid year in year on the original principal. This interest payment method does not take into account the time value money, and is therefore not sustainable.
Compound Interest on the other hand does. Compound interest is when the principal amount changes in order to compensate for the interest earned. If you receive 10% interest each year, that would mean you would get 10% of 1000 (your principal amount). That is 100 rupees at end of the first year. However, interest in 1100 or 110 would be available at the end of year 2.
It is easier to understand continuous compounding when it is compared with other forms interest accumulation. Let's say that a principal of 1 rupee is being compounded bi-annually or twice per year. This formula would look like this:
(1 + 1/2)2 = 2.25
Similar to the above scenario, if the amount was compounded quarterly, the continuous compounding formula would be:
1 + 1/4 = 4.44
We will eventually arrive at the daily compounding amount if we use a similar continuous compounding formula as well as a similar conceptual approach. The following equation would be generated:
(1 + 1/365) = 2.7145
Continuous compounding refers to the compounding interest that occurs every hour, minute and second. Practically, however, we will limit ourselves to a daily compounding rate because the difference is only in decimal points, and of negligible significance.
Continuous compounding is still a theory, and has no practical application in real life. However, it remains an important principle of finance and business.
The continuous compounding formula or continuous compounding interest formula derives its name from the formula used to calculate future value of interest bearing investments. It is as follows.
Future Value (FV = PV x (i / N))(n x T)
The continuous compounding interest formula is then created by applying this concept. The formula continues to repeat until the value "n", or compounding time period, nears infinity. This is because compounding interest can be calculated at even the smallest theoretical intervals, making it theoretical.
FV = PV x e (i x t)
FV stands to future value, while PV stands to present value. i and t stand respectively for interest rate or time. Assume that e is a constant of 2.7183.
Contrary to what you might think, the yields of continuous compounding are not significantly higher than those offered by bi-annual, quarterly, or years. You would get 1500 rupees per year as interest on your initial 10,000 rupees investment at a 15% interest rate. However, continuous compounding would yield you around 1618 rupees. A mere 118 rupees extra.
Continuous compounding may seem to offer a significantly higher yield but it doesn't. Continuous compounding doesn't work in practice. It is a theoretical concept that offers a higher yield, but it rarely manifests in real-world transactions. The interest rate would only be 1% per day if it were to occur. Any lower amounts will result in negligible additional interest.