Gabriel Has $40,000 In A Savings Account That Earns 2% Interest Per Year. The Interest Is Not Compounded. How Much Will He Have In Total In 3 Years?Use The Formula I = P ⋅ R ⋅ T I = P \cdot R \cdot T I = P ⋅ R ⋅ T , Where:- I I I Is The Interest Earned,-

Introduction

In this article, we will explore the concept of simple interest and compound interest, and how they are used to calculate the total amount of money in a savings account over a period of time. We will use a real-life example to illustrate the difference between simple interest and compound interest.

What is Simple Interest?

Simple interest is a type of interest that is calculated on the initial principal amount only. It is not compounded, meaning that the interest is not added to the principal amount at regular intervals. The formula for simple interest is:

$I = P \cdot r \cdot t$

Where:

• $I$ is the interest earned
• $P$ is the principal amount (initial amount of money)
• $r$ is the interest rate (as a decimal)
• $t$ is the time period (in years)

What is Compound Interest?

Compound interest is a type of interest that is calculated on the initial principal amount and any accrued interest. It is compounded, meaning that the interest is added to the principal amount at regular intervals. The formula for compound interest is:

$A = P \cdot (1 + r)^t$

Where:

• $A$ is the total amount of money (principal + interest)
• $P$ is the principal amount (initial amount of money)
• $r$ is the interest rate (as a decimal)
• $t$ is the time period (in years)

Example: Gabriel's Savings Account

Let's use the example of Gabriel, who has $40,000 in a savings account that earns 2% interest per year. The interest is not compounded. We want to find out how much he will have in total in 3 years.

Step 1: Calculate the Interest Earned

Using the formula for simple interest, we can calculate the interest earned as follows:

$I = P \cdot r \cdot t$

$I = 40000 \cdot 0.02 \cdot 3$

$I = 2400$

So, Gabriel will earn $2400 in interest over the 3-year period.

Step 2: Calculate the Total Amount

To find the total amount of money in Gabriel's savings account, we need to add the interest earned to the principal amount:

$A = P + I$

$A = 40000 + 2400$

$A = 42400$

Therefore, Gabriel will have a total of $42400 in his savings account in 3 years.

Conclusion

In this article, we have explored the concept of simple interest and compound interest, and how they are used to calculate the total amount of money in a savings account over a period of time. We have used a real-life example to illustrate the difference between simple interest and compound interest. We have also calculated the interest earned and the total amount of money in Gabriel's savings account over a 3-year period.

Key Takeaways

• Simple interest is calculated on the initial principal amount only, while compound interest is calculated on the initial principal amount and any accrued interest.
• The formula for simple interest is $I = P \cdot r \cdot t$, while the formula for compound interest is $A = P \cdot (1 + r)^t$.
• To calculate the interest earned, we need to multiply the principal amount by the interest rate and the time period.
• To calculate the total amount of money, we need to add the interest earned to the principal amount.

Frequently Asked Questions

• What is the difference between simple interest and compound interest?
• How do I calculate the interest earned using the formula for simple interest?
• How do I calculate the total amount of money using the formula for compound interest?

Answers

• Simple interest is calculated on the initial principal amount only, while compound interest is calculated on the initial principal amount and any accrued interest.
• To calculate the interest earned using the formula for simple interest, we need to multiply the principal amount by the interest rate and the time period.
• To calculate the total amount of money using the formula for compound interest, we need to add the interest earned to the principal amount.

References

• [1] Investopedia. (2022). Simple Interest.
• [2] Investopedia. (2022). Compound Interest.
• [3] Khan Academy. (2022). Simple Interest.
• [4] Khan Academy. (2022). Compound Interest.
  Gabriel's Savings Account: A Q&A Guide =====================================

Introduction

In our previous article, we explored the concept of simple interest and compound interest, and how they are used to calculate the total amount of money in a savings account over a period of time. We used a real-life example to illustrate the difference between simple interest and compound interest. In this article, we will answer some frequently asked questions related to Gabriel's savings account.

Q&A

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

A: Simple interest is calculated on the initial principal amount only, while compound interest is calculated on the initial principal amount and any accrued interest.

Q: How do I calculate the interest earned using the formula for simple interest?

A: To calculate the interest earned using the formula for simple interest, you need to multiply the principal amount by the interest rate and the time period. The formula is:

$I = P \cdot r \cdot t$

Where:

• $I$ is the interest earned
• $P$ is the principal amount (initial amount of money)
• $r$ is the interest rate (as a decimal)
• $t$ is the time period (in years)

Q: How do I calculate the total amount of money using the formula for compound interest?

A: To calculate the total amount of money using the formula for compound interest, you need to add the interest earned to the principal amount. The formula is:

$A = P \cdot (1 + r)^t$

Where:

• $A$ is the total amount of money (principal + interest)
• $P$ is the principal amount (initial amount of money)
• $r$ is the interest rate (as a decimal)
• $t$ is the time period (in years)

Q: What is the interest rate in Gabriel's savings account?

A: The interest rate in Gabriel's savings account is 2% per year.

Q: How much interest will Gabriel earn in 3 years?

A: Using the formula for simple interest, we can calculate the interest earned as follows:

$I = P \cdot r \cdot t$

$I = 40000 \cdot 0.02 \cdot 3$

$I = 2400$

So, Gabriel will earn $2400 in interest over the 3-year period.

Q: How much will Gabriel have in his savings account in 3 years?

A: To find the total amount of money in Gabriel's savings account, we need to add the interest earned to the principal amount:

$A = P + I$

$A = 40000 + 2400$

$A = 42400$

Therefore, Gabriel will have a total of $42400 in his savings account in 3 years.

Q: What is the difference between the total amount of money in Gabriel's savings account and the principal amount?

A: The total amount of money in Gabriel's savings account is $42400, while the principal amount is $40000. The difference is $2400, which is the interest earned over the 3-year period.

Q: How can I calculate the interest earned and the total amount of money in my own savings account?

A: To calculate the interest earned and the total amount of money in your own savings account, you need to use the formulas for simple interest and compound interest. You will need to know the principal amount, interest rate, and time period.

Conclusion

In this article, we have answered some frequently asked questions related to Gabriel's savings account. We have explained the difference between simple interest and compound interest, and how to calculate the interest earned and the total amount of money using the formulas for simple interest and compound interest. We have also provided examples of how to calculate the interest earned and the total amount of money in Gabriel's savings account.

Key Takeaways

• Simple interest is calculated on the initial principal amount only, while compound interest is calculated on the initial principal amount and any accrued interest.
• The formula for simple interest is $I = P \cdot r \cdot t$, while the formula for compound interest is $A = P \cdot (1 + r)^t$.
• To calculate the interest earned, you need to multiply the principal amount by the interest rate and the time period.
• To calculate the total amount of money, you need to add the interest earned to the principal amount.

Frequently Asked Questions

• What is the difference between simple interest and compound interest?
• How do I calculate the interest earned using the formula for simple interest?
• How do I calculate the total amount of money using the formula for compound interest?
• What is the interest rate in Gabriel's savings account?
• How much interest will Gabriel earn in 3 years?
• How much will Gabriel have in his savings account in 3 years?
• What is the difference between the total amount of money in Gabriel's savings account and the principal amount?
• How can I calculate the interest earned and the total amount of money in my own savings account?

Answers

• Simple interest is calculated on the initial principal amount only, while compound interest is calculated on the initial principal amount and any accrued interest.
• To calculate the interest earned using the formula for simple interest, you need to multiply the principal amount by the interest rate and the time period.
• To calculate the total amount of money using the formula for compound interest, you need to add the interest earned to the principal amount.
• The interest rate in Gabriel's savings account is 2% per year.
• Gabriel will earn $2400 in interest over the 3-year period.
• Gabriel will have a total of $42400 in his savings account in 3 years.
• The difference between the total amount of money in Gabriel's savings account and the principal amount is $2400, which is the interest earned over the 3-year period.
• To calculate the interest earned and the total amount of money in your own savings account, you need to use the formulas for simple interest and compound interest. You will need to know the principal amount, interest rate, and time period.