Grace Deposited $1500 Into A New Bank Account. It Earns 4.5% Annual Simple Interest. What Is The Balance Of The Account After 5 Years? Do Not Include A Dollar Sign With Your Answer.

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What is Simple Interest?

Simple interest is a type of interest that is calculated only on the initial principal amount deposited into an account. It does not take into account the interest that has accrued over time. In other words, simple interest is calculated as a percentage of the principal amount, and it is added to the principal amount to determine the new balance.

Calculating Simple Interest

The formula for calculating simple interest is:

Simple Interest = Principal x Rate x Time

Where:

  • Principal is the initial amount deposited into the account
  • Rate is the annual interest rate as a decimal
  • Time is the number of years the money is invested

Calculating the Balance of the Account

In this problem, Grace deposited $1500 into a new bank account that earns 4.5% annual simple interest. We need to calculate the balance of the account after 5 years.

First, we need to convert the annual interest rate from a percentage to a decimal:

4.5% = 0.045

Next, we can plug in the values into the simple interest formula:

Simple Interest = 1500 x 0.045 x 5

Simple Interest = 3375

Now, we need to add the simple interest to the principal amount to determine the new balance:

Balance = Principal + Simple Interest = 1500 + 3375 = 4875

Conclusion

After 5 years, the balance of the account will be $4875. This is the total amount that will be in the account, including the initial principal amount and the interest that has accrued over time.

Why is Simple Interest Important?

Simple interest is an important concept in finance because it helps individuals and businesses understand how interest is calculated on loans and investments. It is also used to determine the interest rate on savings accounts and other types of investments.

Real-World Applications of Simple Interest

Simple interest has many real-world applications, including:

  • Calculating interest on loans and credit cards
  • Determining the interest rate on savings accounts and other types of investments
  • Understanding how interest is calculated on investments such as bonds and stocks
  • Calculating the interest on a mortgage or other type of loan

Tips for Calculating Simple Interest

When calculating simple interest, it is essential to remember the following tips:

  • Always convert the annual interest rate from a percentage to a decimal
  • Use the simple interest formula to calculate the interest
  • Add the simple interest to the principal amount to determine the new balance
  • Consider using a calculator or spreadsheet to make the calculation easier

Common Mistakes to Avoid When Calculating Simple Interest

When calculating simple interest, it is essential to avoid the following common mistakes:

  • Forgetting to convert the annual interest rate from a percentage to a decimal
  • Using the wrong formula or calculation method
  • Not adding the simple interest to the principal amount
  • Not considering the time value of money when calculating interest

Conclusion

Frequently Asked Questions About Simple Interest

Q: What is the difference between simple interest and compound interest?

A: Simple interest is calculated only on the initial principal amount, while compound interest is calculated on both the principal amount and any accrued interest. This means that compound interest can result in a higher balance over time.

Q: How do I calculate simple interest on a loan or investment?

A: To calculate simple interest, you need to know the principal amount, the annual interest rate, and the time period. You can use the simple interest formula: Simple Interest = Principal x Rate x Time.

Q: What is the formula for calculating simple interest?

A: The formula for calculating simple interest is:

Simple Interest = Principal x Rate x Time

Where:

  • Principal is the initial amount deposited into the account
  • Rate is the annual interest rate as a decimal
  • Time is the number of years the money is invested

Q: How do I convert a percentage to a decimal?

A: To convert a percentage to a decimal, you need to divide the percentage by 100. For example, 4.5% = 0.045.

Q: What is the difference between annual and monthly interest rates?

A: The annual interest rate is the rate charged over a year, while the monthly interest rate is the rate charged over a month. To calculate the monthly interest rate, you need to divide the annual interest rate by 12.

Q: Can I use a calculator or spreadsheet to calculate simple interest?

A: Yes, you can use a calculator or spreadsheet to make the calculation easier. Many calculators and spreadsheets have built-in functions for calculating simple interest.

Q: What are some common mistakes to avoid when calculating simple interest?

A: Some common mistakes to avoid when calculating simple interest include:

  • Forgetting to convert the annual interest rate from a percentage to a decimal
  • Using the wrong formula or calculation method
  • Not adding the simple interest to the principal amount
  • Not considering the time value of money when calculating interest

Q: How do I determine the interest rate on a savings account or other type of investment?

A: The interest rate on a savings account or other type of investment is usually stated as a percentage. You can convert this percentage to a decimal by dividing it by 100.

Q: Can I use simple interest to calculate the interest on a mortgage or other type of loan?

A: Yes, you can use simple interest to calculate the interest on a mortgage or other type of loan. However, you may need to consider other factors such as compounding interest and fees.

Q: What are some real-world applications of simple interest?

A: Simple interest has many real-world applications, including:

  • Calculating interest on loans and credit cards
  • Determining the interest rate on savings accounts and other types of investments
  • Understanding how interest is calculated on investments such as bonds and stocks
  • Calculating the interest on a mortgage or other type of loan

Q: How do I use simple interest to make informed decisions about my finances?

A: You can use simple interest to make informed decisions about your finances by:

  • Calculating the interest on your loans and investments
  • Comparing interest rates on different savings accounts and investments
  • Understanding how interest is calculated on your mortgage or other type of loan
  • Considering the time value of money when making financial decisions

Conclusion

In conclusion, simple interest is an essential concept in finance that helps individuals and businesses understand how interest is calculated on loans and investments. By understanding how to calculate simple interest, you can make informed decisions about your finances and achieve your financial goals.