Certain investments compound interest at different intervals. What effect does the size of the compounding interval have on the yield of the investment?
take a look at the graph of
(1+.10/n)^(n)
It shows the effective yield of 10% compounded n times per year.
It approaches continuous compounding, e^.1
http://www.wolframalpha.com/input/?i=plot+y%3D%281%2B.1%2Fn%29^n+for+n+%3D+1..40%2C+y%3De^.1
The size of the compounding interval has an impact on the yield of the investment. Generally, the more frequent the compounding, the higher the yield will be. This is because compound interest calculates interest on both the initial principal and the accumulated interest from previous periods. By compounding more often, the interest is reinvested more frequently, leading to exponential growth.
To understand this concept, consider the following example: Let's say you have $1,000 invested with a 5% annual interest rate.
If the investment compounds annually, at the end of the year, you would earn $50 in interest, resulting in a new balance of $1,050.
However, if the investment compounds semi-annually, the compounding occurs twice a year. In the first six months, you would earn $25 in interest, resulting in a new balance of $1,025. For the next six months, the interest is then calculated on the new balance of $1,025, leading to an additional $25.63 in interest. This gives you a total interest of $50.63, resulting in a new balance of $1,050.63.
As you can see, compounding more often leads to slightly higher returns. The effect becomes more significant when the compounding interval becomes smaller, such as quarterly, monthly, or daily compounding.
To calculate the yield of an investment with different compounding intervals, you can use the compound interest formula:
A = P(1 + r/n)^(nt)
Where:
- A is the ending balance or yield
- P is the principal amount (initial investment)
- r is the annual interest rate (expressed as a decimal)
- n is the number of compounding periods per year
- t is the time (in years)
By plugging in different values for n, you can compare the yields for different compounding intervals.
In summary, the size of the compounding interval directly affects the yield of an investment. The more frequently interest is compounded, the higher the yield will be, leading to potentially greater returns over time.
The size of the compounding interval can have a significant effect on the yield of an investment. Generally, more frequent compounding results in higher yields. When interest is compounded more frequently, such as daily or monthly, the investment has the opportunity to grow more rapidly since the interest is added to the principal more frequently.
For example, consider two investments with the same interest rate and duration, but one compounds annually and the other compounds quarterly. The investment that compounds quarterly will have higher yields because it earns interest four times a year, allowing the interest to be reinvested and earn more interest.
In essence, the more frequently interest is compounded, the more compounding periods there are in a given timeframe, which leads to higher overall yields for the investment. Therefore, choosing an investment with smaller compounding intervals can result in greater returns over time.