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The future value of an investment is essentially how much money you will have in total at the end of an investment period, after accounting for the accumulated interest. It's the total amount that your initial investment has grown to, after being subjected to compound interest over time. When calculating future value, you're determining how much a present amount of money will be worth in the future, given a specific interest rate and time duration.

This is particularly useful when planning for long-term financial goals, like retirement or buying a house, because it helps you understand how your money can grow over time. Future value gives you a clear picture of what your investments today can achieve in the future. In our example, Devon's investment grows from $25,000 to a future value of approximately $67,574.75 over 15 years.

By understanding future value, you can make informed decisions about where and how to invest your money, ensuring it aligns with your financial goals and time frames.

Interest calculation is an essential part of understanding how investments grow. With compound interest, you're not just earning interest on your principal amount but also on the interest that has been added to it over previous periods. This is what makes compound interest so powerful compared to simple interest.

In the exercise, Devon's investment is subject to a 6.5% annual interest rate compounded quarterly. Let's break this down:

• The annual rate of 6.5% is split into quarters because the interest compounds quarterly. This means each quarter, you earn 1.625% (which is 6.5% divided by 4) on the current account balance.
• Over 15 years, this results in 60 compounding periods (4 quarters per year times 15 years).

Understanding how the interest is calculated period by period helps you comprehend how quickly your investment might grow and the effects of different compounding frequencies on that growth.

The investment formula to calculate the future value with compound interest is a cornerstone of financial mathematics. It's:\[FV = P \times \left(1 + \frac{r}{n}\right)^{n \times t}\]Here's how each variable in the formula represents elements of your investment:

• \(P\) represents the principal amount, or the initial amount of money invested or borrowed.
• \(r\) is the annual interest rate as a decimal. So, 6.5% becomes 0.065.
• \(n\) is the number of times the interest is compounded per year. For example, quarterly compounding has \(n = 4\).
• \(t\) is the number of years the money is invested or borrowed.

The investment formula helps you understand how an investment grows over time with compounding. It allows you to predict the future growth of your money based on your current investment strategy. Mastering this formula can equip you with the tools you need to make smarter financial decisions.