Question

If you deposit \(\$ 500\) in a savings account that offers 3 percent interest, compounded annually, and you don't withdraw any money, how much money should you expect to have in the account at the end of three years?

Short answer

After three years, you will have approximately \( 546.36 \) dollars in the account.

Step-by-step solution

Identify the given values and the formula

We know the principal (initial amount) deposited is \( P = 500 \) dollars, the annual interest rate is \( r = 0.03 \) (or 3%), and the time period is \( t = 3 \) years. The formula for compound interest is given by: \[ A = P (1 + r)^t \] where \( A \) is the amount of money accumulated after \( t \) years, including interest.

Substitute the values into the formula

Substitute the given values into the compound interest formula: \[ A = 500 (1 + 0.03)^3 \] This expression will help us calculate the amount of money accumulated after three years.

Calculate the compound interest

First, calculate \( (1 + 0.03)^3 \):\[ (1 + 0.03)^3 = 1.03^3 = 1.092727 \] (rounded to six decimal places). Next, multiply by the principal \( P = 500 \):\[ A = 500 \times 1.092727 = 546.36 \] Thus, the total amount in the account after three years is approximately \( 546.36 \) dollars.

Key concepts

Understanding a Savings Account

A savings account is like a safe place for your money to grow. When you deposit money into a savings account, the bank rewards you with interest for keeping your money there. This makes a savings account a great way to save money while earning a little extra over time.

Here are some key things you should know about savings accounts:

• Security: Most savings accounts are insured by the government, meaning your money is protected.
• Interest Earnings: The money you keep in the account earns interest, allowing your savings to grow.
• Accessibility: Although it's not meant for daily use, you can usually withdraw your money when needed.

This makes a savings account a practical choice for achieving financial goals over the long term.

What is an Interest Rate?

An interest rate is the percentage at which your savings increase over a certain period. Banks use this rate to calculate how much extra money you'll earn on the amount you save. Interest can be thought of as the cost of borrowing money or, in terms of savings, the reward for saving money.


There are different types of interest rates:

• Simple Interest: This type of interest is calculated only on the principal amount.
• Compound Interest: In this case, interest is calculated on both the initial principal and the accumulated interest from previous periods.

In our case, we are dealing with compound interest, which means your savings grow at an increasing rate each year—offering a snowball effect of sorts where each year's earnings build on the last.

The Role of the Principal Amount

The principal amount is the initial sum of money you deposit or invest in a savings account or any investment. It's the base amount on which interest is calculated.

In our example, the principal amount is the \(500\) dollars deposited into the account. The principal serves as the foundation for how much interest you will earn. Greater principal amounts will earn higher returns assuming the interest rate and the time period remain constant.

Why is the principal so important? Because:

• Starting Point: It sets the baseline for calculating interest.
• Growth Potential: The more you save initially, the more interest you accrue over time.

By understanding the role of the principal, you can better strategize your savings goals and choose how much to deposit for your desired growth.