Ellen Has $20,000 In A Savings Account That Earns 3% Interest Per Year. The Interest Is Not Compounded. How Much Will She Have In Total In 5 Years?Use The Formula I = P R T I = Prt I = P R T , Where:- I I I Is The Interest Earned,- P P P Is The

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Understanding Simple Interest

Simple interest is a type of interest that is calculated only on the initial principal amount, without taking into account the interest that has already accrued. In this scenario, Ellen has $20,000 in a savings account that earns a 3% interest rate per year, and the interest is not compounded. This means that the interest earned in each year will be calculated only on the initial principal amount, and not on the total balance.

The Formula for Simple Interest

The formula for simple interest is given by:

I=prtI = prt

Where:

  • II is the interest earned
  • pp is the principal amount (initial amount)
  • rr is the interest rate per time period
  • tt is the time period (in years)

Calculating Interest for Each Year

To calculate the total amount Ellen will have in 5 years, we need to calculate the interest earned for each year and add it to the principal amount.

Year 1: Interest earned = $20,000 x 3% x 1 year = $600 Total balance = $20,000 + $600 = $20,600

Year 2: Interest earned = $20,600 x 3% x 1 year = $618 Total balance = $20,600 + $618 = $21,218

Year 3: Interest earned = $21,218 x 3% x 1 year = $636 Total balance = $21,218 + $636 = $21,854

Year 4: Interest earned = $21,854 x 3% x 1 year = $655 Total balance = $21,854 + $655 = $22,509

Year 5: Interest earned = $22,509 x 3% x 1 year = $675 Total balance = $22,509 + $675 = $23,184

Total Amount after 5 Years

After 5 years, Ellen will have a total of $23,184 in her savings account.

Conclusion

In this scenario, we calculated the total amount Ellen will have in 5 years using the formula for simple interest. We found that the interest earned in each year is calculated only on the initial principal amount, and not on the total balance. By adding the interest earned in each year to the principal amount, we were able to determine the total amount after 5 years.

Real-World Applications

Understanding simple interest is crucial in real-world applications such as:

  • Calculating interest on loans and credit cards
  • Determining the return on investment (ROI) for investments
  • Calculating the future value of savings accounts and other investments

By applying the formula for simple interest, individuals can make informed decisions about their financial investments and savings.

Tips and Variations

  • To calculate the interest earned on a loan or credit card, use the formula I=prtI = prt and add the interest to the principal amount.
  • To calculate the return on investment (ROI) for an investment, use the formula ROI=(I/P)x100ROI = (I / P) x 100.
  • To calculate the future value of a savings account or other investment, use the formula FV=P+IFV = P + I.

Q: What is simple interest?

A: Simple interest is a type of interest that is calculated only on the initial principal amount, without taking into account the interest that has already accrued.

Q: How is simple interest calculated?

A: The formula for simple interest is given by:

I=prtI = prt

Where:

  • II is the interest earned
  • pp is the principal amount (initial amount)
  • rr is the interest rate per time period
  • tt is the time period (in years)

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

A: The main difference between simple interest and compound interest is that simple interest is calculated only on the initial principal amount, while compound interest is calculated on the total balance, including the interest earned.

Q: How do I calculate the interest earned on a loan or credit card?

A: To calculate the interest earned on a loan or credit card, use the formula I=prtI = prt and add the interest to the principal amount.

Q: How do I calculate the return on investment (ROI) for an investment?

A: To calculate the return on investment (ROI) for an investment, use the formula ROI=(I/P)x100ROI = (I / P) x 100.

Q: How do I calculate the future value of a savings account or other investment?

A: To calculate the future value of a savings account or other investment, use the formula FV=P+IFV = P + I.

Q: What is the formula for compound interest?

A: The formula for compound interest is given by:

A=P(1+r)tA = P(1 + r)^t

Where:

  • AA is the future value
  • PP is the principal amount (initial amount)
  • rr is the interest rate per time period
  • tt is the time period (in years)

Q: How do I calculate the interest earned on a savings account with compound interest?

A: To calculate the interest earned on a savings account with compound interest, use the formula A=P(1+r)tA = P(1 + r)^t and subtract the principal amount from the future value.

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

A: Yes, you can use a calculator to calculate simple interest. Simply enter the principal amount, interest rate, and time period, and the calculator will give you the interest earned.

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

A: Yes, you can use a spreadsheet to calculate simple interest. Simply enter the principal amount, interest rate, and time period in the spreadsheet, and the spreadsheet will give you the interest earned.

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

A: Some real-world applications of simple interest include:

  • Calculating interest on loans and credit cards
  • Determining the return on investment (ROI) for investments
  • Calculating the future value of savings accounts and other investments
  • Calculating the interest earned on a savings account with compound interest

By understanding simple interest and applying the formula, individuals can make informed decisions about their financial investments and savings.