Question

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

Short answer

The future value of Angela's money in one year is $1,030.

Step-by-step solution

Understanding the Interest

Angela has put $1,000 in an account that pays 3% interest per year. This means that we need to calculate how much additional money she will have from the interest at the end of one year.

Calculating the Interest

To find the interest earned, we multiply the principal amount, $1,000, by the interest rate, which is 3%. This can be found using the formula: Interest = Principal \( \times \) Rate. Substituting the known values: Interest = 1,000 \( \times \) 0.03 = 30 dollars.

Calculating the Future Value

The future value of Angela's money after one year is the sum of the original principal and the interest earned. Thus, Future Value = Principal + Interest. Substituting the values: Future Value = 1,000 + 30 = 1,030 dollars.

Key concepts

Simple Interest

Simple interest is a method to calculate the extra amount you can earn on an initial investment, known as the principal, over a specified period. Unlike compound interest, which calculates interest on previously earned interest, simple interest is only calculated on the principal amount itself. For example, if you have a savings account, the bank will calculate interest based only on the amount you initially deposited. This makes it an easy way to understand how much money you will gain over time without compounding. The formula for simple interest is:

• Interest = Principal \( \times \) Rate \( \times \) Time

To find out how much interest Angela would earn from her savings, we multiply her initial deposit by the interest rate. Since the interest is calculated only once on the principal, it is straightforward and predictable. This simplicity makes it appealing for short-term investments or savings.

Principal Amount

The principal amount is the initial sum of money that you deposit or invest on which interest will be calculated. In Angela's case, her principal amount is $1,000. Understanding the principal is crucial in any financial decision because it is the starting point for most calculations.
When you deposit money in a savings account, the principal amount is the initial cash you put in. It is important to keep track of your principal because all future interest calculations will be based on this amount.
In many financial situations, the larger your principal, the more interest you will earn over time. Thus, ensuring a good principal amount can significantly affect your future savings or investment returns.

Interest Rate

An interest rate is the percentage at which interest is paid by borrowers for the use of money they borrow from a lender, or the percentage paid to investors who deposit money in an account. In Angela's example, the account offers an interest rate of 3% per year. This means for every $100 of principal, Angela earns $3 in interest after a year.

• The interest rate determines the growth of your investment or savings over time.
• Interest rates may vary depending on the risk, the type of account, and economic conditions.

It is important to understand how interest rates work, as they heavily influence your potential earnings from savings accounts and investments. A higher interest rate can significantly boost your savings over time, so monitoring and comparing rates is important for making sound financial decisions.

Financial Literacy

Financial literacy refers to the understanding and effective use of various financial skills, including personal financial management, budgeting, and investing. Angela's decision to invest in a savings account with a 3% interest rate reflects her level of financial literacy.

• Being financially literate allows individuals to make informed decisions about saving and investing.
• It helps in understanding the impact of interest rates, both simple and compound, on personal finances.

A strong foundation in financial literacy can help you achieve your financial goals, such as saving for college, buying a home, or investing for retirement. Understanding concepts like simple interest and the importance of the principal amount can empower you to make better financial decisions and grow your wealth over time.