Question

Angela puts \(\$ 1,000\) in a savings account that pays 3 percent per year. What is the future value of her money one year from now? a. \(\$ 970\) b. \(\$ 1,000\) c. \(\$ 1,003\) d. \(\$ 1,030\)

Short answer

The future value of Angela's money one year from now is \( \$ 1,030 \).

Step-by-step solution

Understand the Problem

We need to calculate the future value of an investment of $1,000 in a savings account that earns 3% interest per year. We are interested in the value of this investment one year from now.

Identify the Formula

The formula to calculate the future value of an investment with simple interest is: \( FV = P \times (1 + r) \), where \( FV \) is the future value, \( P \) is the principal amount, and \( r \) is the interest rate.

Substitute the Known Values

In our case, \( P = 1000 \), and \( r = 0.03 \) (since 3% is equivalent to 0.03 when expressed as a decimal). Substitute these values into the formula: \( FV = 1000 \times (1 + 0.03) \).

Perform the Calculation

Calculate the expression: \( 1000 \times 1.03 = 1030 \).

Select the Correct Option

The calculated future value is \( 1,030 \). Refer to the provided options; the answer matches option d. \( \$ 1,030 \).

Key concepts

Understanding Simple Interest

Simple interest is a straightforward way of calculating the interest earned on an investment. It is called 'simple' because the interest is not compounded; that means it's calculated only on the original principal, rather than on accumulated interest from previous periods. This makes the calculation easier and the results predictable.

The formula for simple interest is expressed as:
\[ FV = P \times (1 + r) \]
Here, \( FV \) stands for future value, \( P \) is the principal amount, and \( r \) is the interest rate. By understanding this formula, you can easily determine how much an investment will grow over a specified period.

Simple interest is often used for short-term investments or loans, where the period doesn't extend to years, as it doesn't account for compounding effects.

Basics of Investment Calculations

Investment calculations are essential for understanding how much your money will grow over time. They also help in assessing whether an investment option is good based on the potential returns compared to other choices. Knowing these calculations can guide you in making informed financial decisions.

When performing investment calculations, it's important to:

• Identify the principal amount, which is the initial sum of money invested.
• Know the interest rate, which determines how quickly your investment will grow.
• Define the time period for which you're letting your investment grow.

Using these parameters, you can utilize formulas like the simple interest formula to ascertain the future value of your investments. This preparation will help in evaluating multiple investment scenarios and understanding how changes in any of these factors affect your investment's final outcome.

Calculating Interest Rate

An interest rate is a critical component of investment calculations, indicating the percent increase of your investment over a specified period. In the context of simple interest, the interest rate is a flat rate applied to the initial principal.

To calculate the interest rate for an investment, it’s often given as a percentage. For calculations, you need to convert this percentage into a decimal by dividing by 100. For example, a 3% interest rate becomes \( 0.03 \). This conversion is essential to avoid errors in your investment calculations. Understanding the interest rate's role helps you predict how your investment increases over time and compare with potential returns from different investment opportunities.

Defining the Principal Amount

The principal amount, often just called the principal, is the original sum of money that you invest or save before any interest is added. In any investment or savings account, this is the base value that the interest is calculated on.

It's important to clearly define the principal amount in any investment. In our example, the principal amount is \( \$1000 \). This clarity allows you to apply the appropriate formulas for calculating future value, as setting the right principal is the starting point for any investment scenario.

Knowing your principal is essential because it helps determine the real growth of your investment. Without an accurate understanding of your principal, any calculated future value would be unreliable.