Compound Interest: Calculate Investment Growth Over 9 Years

Nov 14, 2025 by Alex Johnson 60 views

Understanding compound interest is crucial for making informed financial decisions. This article will guide you through calculating the future value of an investment, specifically focusing on a scenario where $200 is deposited into an account with a 6% annual interest rate, compounded weekly, over a period of 9 years. We'll break down the formula, explain each component, and walk through the calculation step-by-step.

Understanding Compound Interest

Compound interest is often referred to as the eighth wonder of the world, and for good reason. It’s the interest you earn not only on your initial deposit, also known as the principal, but also on the interest that has already been added to the account. This means your money grows at an accelerating rate over time. The more frequently the interest is compounded (e.g., daily, weekly, monthly), the faster your money grows.

The Compound Interest Formula

The formula for calculating compound interest is:

$A = P(1 + \frac{r}{k})^{kt}$

Where:

$A$ is the accumulated amount (the future value of the investment).
$P$ is the principal amount (the initial deposit).
$r$ is the annual interest rate (as a decimal).
$k$ is the number of times the interest is compounded per year.
$t$ is the number of years the money is invested.

Let’s break down each component of this formula and understand its role in the calculation.

A (Accumulated Amount): This is what we're trying to find – the total amount of money you'll have at the end of the investment period, including both the principal and the accumulated interest.
P (Principal Amount): This is the initial amount of money you deposit. In our example, this is $200. The principal is the foundation upon which your investment grows.
r (Annual Interest Rate): This is the stated interest rate for the entire year, expressed as a decimal. For instance, a 6% interest rate is written as 0.06. This rate is crucial in determining how quickly your investment will grow.
k (Number of Times Interest is Compounded Per Year): This indicates how often the interest is calculated and added to the account balance each year. The more frequently interest is compounded, the greater the overall return due to the effect of earning interest on previously earned interest. In our scenario, the interest is compounded weekly, so k = 52.
t (Number of Years): This is the length of time the money is invested. In our case, this is 9 years. The longer the investment period, the more significant the impact of compound interest.

Applying the Formula to Our Scenario

Now, let’s apply this formula to the specific scenario provided: a $200 deposit with a 6% interest rate, compounded weekly (52 times per year), over 9 years.

$P = $200$
$r = 6% = 0.06$
$k = 52$ (compounded weekly)
$t = 9$ years

Plugging these values into the formula, we get:

$A = 200(1 + \frac{0.06}{52})^{52 imes 9}$

Let's break this down step-by-step:

Calculate the value inside the parentheses: $\frac{0.06}{52} \approx 0.0011538$ . Then, add 1: $1 + 0.0011538 = 1.0011538$ .
Calculate the exponent: $52 imes 9 = 468$ .
Raise the value from step 1 to the power of the exponent from step 2: $1.0011538^{468} \approx 1.71278$ .
Multiply the result by the principal amount: $200 imes 1.71278 \approx 342.56$ .

Therefore, the accumulated amount after 9 years is approximately $342.56.

Step-by-Step Calculation Breakdown

To further clarify the calculation, let's break it down into smaller, more manageable steps:

Calculate the weekly interest rate: Divide the annual interest rate by the number of compounding periods per year: $0.06 / 52 \approx 0.0011538$ .
Add the weekly interest rate to 1: This represents the growth factor for each week: $1 + 0.0011538 = 1.0011538$ .
Calculate the total number of compounding periods: Multiply the number of compounding periods per year by the number of years: $52 imes 9 = 468$ .
Raise the growth factor (from step 2) to the power of the total number of compounding periods (from step 3): This calculates the overall growth over the entire investment period: $1.0011538^{468} \approx 1.71278$ .
Multiply the result (from step 4) by the principal amount: This gives you the accumulated amount after 9 years: $200 imes 1.71278 \approx $342.56$ .

The Impact of Compounding Frequency

It's important to understand that the frequency of compounding significantly impacts the final accumulated amount. In this example, we compounded weekly. If the interest were compounded monthly (k = 12) or annually (k = 1), the accumulated amount would be different.

To illustrate this, let's calculate the accumulated amount with annual compounding:

$A = 200(1 + \frac{0.06}{1})^{1 imes 9}$ $A = 200(1 + 0.06)^9$ $A = 200(1.06)^9$ $A \approx 200 imes 1.68948$ $A \approx $337.90$

As you can see, compounding weekly results in a higher accumulated amount ($342.56) compared to compounding annually ($337.90). This difference, while seemingly small in this example, can become quite substantial over longer investment periods and with larger principal amounts.

Key Takeaways

Compound interest is a powerful tool for wealth accumulation.
The formula $A = P(1 + \frac{r}{k})^{kt}$ is used to calculate the future value of an investment with compound interest.
The frequency of compounding significantly affects the final accumulated amount. More frequent compounding leads to higher returns.
Understanding and utilizing compound interest is crucial for making sound financial decisions.

Conclusion

Calculating compound interest might seem daunting at first, but by breaking down the formula and understanding each component, it becomes a manageable process. In our example, a $200 deposit with a 6% interest rate, compounded weekly, grows to approximately $342.56 after 9 years. This demonstrates the power of compound interest and highlights the importance of starting to save and invest early. Remember that consistent contributions and a long-term perspective are key to maximizing the benefits of compounding. Don't hesitate to explore different scenarios and play around with the variables in the formula to understand how they impact your investment growth. For more detailed information and advanced calculators, you can visit websites like Investopedia's Compound Interest Calculator to further enhance your understanding.