Understanding Compound Interest: Exploring the Growth of 900 at 4% Per Annum
Compound interest is a powerful financial concept that can significantly enhance the growth of your capital over time. In this article, we will delve into how compound interest on a principal amount of $900 at an annual percentage rate (APR) of 4% can evolve over a span of 123 years, considering 4 compounding periods per year. We will break down the calculation process and illustrate how the interest accumulates, leading to substantial growth.
Compound Interest Formula
The compound interest formula is given by:
FV P(1 r/n) ^ (nt)
Where: FV is the future value of the investment P is the principal amount (initial investment) r is the annual interest rate (in decimal form) n is the number of times interest is compounded per year t is the number of years
A Case Study: Compound Interest on $900 at 4% APR
For our example, let's calculate the future value of $900 (P 900) at an annual interest rate of 4% (r 0.04) with 4 compounding periods per year (n 4) over a period of 123 years (t 123).
Year 1
Now, let's calculate the future value for the first year.
FV 900(1 0.04/4)^(4*1)
FV 900(1 0.01)^4
FV 900(1.01)^4 ≈ 936.54
The interest for the first year is:
Interest 936.54 - 900 36.54
Year 2 and Beyond
For subsequent years, the future value will be calculated using the new principal amount.
Year 2
FV 936.54(1 0.04/4)^(4*1)
FV 936.54(1 0.01)^4 ≈ 974.57
The interest for the second year is:
Interest 974.57 - 936.54 38.03
Year 3 and Beyond
The process repeats for each subsequent year.
Year 3
FV 974.57(1 0.04/4)^(4*1)
FV 974.57(1 0.01)^4 ≈ 1014.14
The interest for the third year is:
Interest 1014.14 - 974.57 39.57
General Formula for Future Value Calculation
To generalize the future value calculation for any year, you can use:
FV_n 900(1 0.01)^(4n)
Where n is the number of years.
Key Takeaways
Compounding interest is a powerful financial tool that helps your money grow over time. Here are some key points to remember: The more frequent the compounding periods (e.g., monthly, quarterly, annually), the more the growth of your investment. The time (t) also plays a crucial role; the longer the investment period, the more significant the growth. Understanding the compound interest formula can help you make informed financial decisions.
Additional Resources
Likewise, for a more in-depth explanation and practical applications of compound interest, consider reading comprehensive articles or consulting with a financial advisor. Look up ‘compound interest’ on Google for more resources and examples.