What is Compounding Interest?

Compounding interest is the process where the interest you earn on an investment is reinvested, so that in subsequent periods, interest is earned on both the initial principal and the previously accumulated interest. This snowball effect can lead to exponential growth of your investments over time.

For example, if you invest $1,000 at an annual interest rate of 5%, after one year you will have $1,050. In the second year, you will earn interest not only on your original $1,000 but also on the $50 interest from the first year, resulting in $1,102.50 at the end of the second year. As this process continues, your investment can grow significantly.

The Difference 10 Years Makes

To truly grasp the power of compounding interest, let's look at a scenario where two individuals, Alice and Bob, start investing at different times. Alice begins investing $5,000 per year at age 25 and continues until she reaches 35, then stops contributing but leaves her investments to grow. Bob, on the other hand, starts investing $5,000 per year at age 35 and continues until he reaches 65. Both earn an average annual return of 7%.

Alice's Investment:

• Starts at age 25, stops at age 35 (10 years of contributions)
• Total contributions: $5,000 x 10 years = $50,000
• Investment grows for 40 years (until age 65)

Bob's Investment:

• Starts at age 35, stops at age 65 (30 years of contributions)
• Total contributions: $5,000 x 30 years = $150,000
• Investment grows for 30 years (until age 65)

Despite contributing significantly less, Alice's investment benefits from an additional 10 years of compounding. Let's see how their investments grow over time.

The Math Behind Compounding

Using the formula for compound interest:

A=P(1+rn)ntA = P \left(1 + \frac{r}{n}\right)^{nt}A=P(1+nr​)nt

Where:

• AAA = the amount of money accumulated after n years, including interest.
• PPP = the principal amount (initial investment).
• rrr = annual interest rate (decimal).
• nnn = number of times that interest is compounded per year.
• ttt = the number of years the money is invested.

For simplicity, let's assume the interest is compounded once per year (n=1n = 1n=1).

Alice's Final Amount:

• P=5,000×10=50,000P = 5,000 \times 10 = 50,000P=5,000×10=50,000
• r=0.07r = 0.07r=0.07
• t=40t = 40t=40 (since her last contribution is at age 35, and she lets it grow until age 65)

$748,500

Bob's Final Amount:

• P=5,000×30=150,000P = 5,000 \times 30 = 150,000P=5,000×30=150,000
• r=0.07r = 0.07r=0.07
• t=30t = 30t=30

$1,141,500

While Bob ends up with more money overall due to his higher contributions, the power of compounding significantly amplifies Alice's smaller investment over a longer period.

The Bottom Line

Alice’s early start allows her to achieve remarkable growth with less than half the contributions of Bob. This scenario demonstrates the critical importance of starting to invest as early as possible. The extra decade of compounding interest gives Alice’s investment the time it needs to grow exponentially.

In conclusion, the power of compounding interest underscores the value of time in investing. Starting early, even with smaller amounts, can lead to substantial wealth accumulation over the long term. If you're considering investing, the best time to start is now. By giving your money more time to grow, you can harness the full potential of compounding interest and achieve your financial goals more effectively.