Kari Has $89,250 In A Savings Account That Earns 13% Interest Per Year. The Interest Is Not Compounded. How Much Interest Will She Earn In 8 Months?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

Understanding the Problem

Kari has a significant amount of money saved in a savings account, with a principal amount of $89,250. The account earns a 13% interest rate per year, but the interest is not compounded. In this scenario, we need to calculate the interest earned by Kari in 8 months.

The Formula for Interest Earned

The formula to calculate the interest earned is given by:

$$i = prt$$

where:

• $i$ is the interest earned
• $p$ is the principal amount (initial amount of money)
• $r$ is the interest rate (in decimal form)
• $t$ is the time period (in years)

Converting Time Period to Years

Since the interest rate is given per year, we need to convert the time period of 8 months to years. There are 12 months in a year, so:

$$8 \text{ months} = \frac{8}{12} = \frac{2}{3} \text{ years}$$

Applying the Formula

Now, we can apply the formula to calculate the interest earned:

$$i = prt$$

$$i = 89250 \times 0.13 \times \frac{2}{3}$$

Calculating the Interest Earned

To calculate the interest earned, we need to multiply the principal amount, interest rate, and time period:

$$i = 89250 \times 0.13 \times \frac{2}{3}$$

$$i = 89250 \times 0.08667$$

$$i = 7755.75$$

Conclusion

Therefore, Kari will earn approximately $7755.75 in interest in 8 months, assuming the interest rate remains constant and is not compounded.

Understanding the Importance of Compounding Interest

It's worth noting that the interest is not compounded in this scenario. Compounding interest means that the interest earned is added to the principal amount, and then the interest rate is applied to the new principal amount. This can result in a higher interest earned over time.

Example of Compounding Interest

To illustrate the effect of compounding interest, let's consider an example. Suppose Kari has the same principal amount of $89,250, but the interest is compounded annually at a 13% interest rate. In this case, the interest earned would be:

$$i = 89250 \times 0.13 \times 1$$

$$i = 11612.5$$

As you can see, the interest earned is significantly higher when the interest is compounded annually.

Conclusion

In conclusion, Kari will earn approximately $7755.75 in interest in 8 months, assuming the interest rate remains constant and is not compounded. However, if the interest is compounded annually, the interest earned would be significantly higher.

Key Takeaways

• The formula to calculate interest earned is given by $i = prt$
• The interest rate should be in decimal form
• The time period should be in years
• Compounding interest can result in a higher interest earned over time

Frequently Asked Questions

Q: What is the formula to calculate interest earned?

A: The formula to calculate interest earned is given by $i = prt$, where $i$ is the interest earned, $p$ is the principal amount, $r$ is the interest rate, and $t$ is the time period.

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

A: Simple interest means that the interest earned is not added to the principal amount, while compound interest means that the interest earned is added to the principal amount, and then the interest rate is applied to the new principal amount.

Q: How can I calculate the interest earned on a savings account?

A: You can use the formula $i = prt$ to calculate the interest earned, where $i$ is the interest earned, $p$ is the principal amount, $r$ is the interest rate, and $t$ is the time period.

Q: What is the importance of compounding interest?

Q: What is the formula to calculate interest earned?

A: The formula to calculate interest earned is given by $i = prt$, where $i$ is the interest earned, $p$ is the principal amount, $r$ is the interest rate, and $t$ is the time period.

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

A: Simple interest means that the interest earned is not added to the principal amount, while compound interest means that the interest earned is added to the principal amount, and then the interest rate is applied to the new principal amount.

Q: How can I calculate the interest earned on a savings account?

A: You can use the formula $i = prt$ to calculate the interest earned, where $i$ is the interest earned, $p$ is the principal amount, $r$ is the interest rate, and $t$ is the time period.

Q: What is the importance of compounding interest?

A: Compounding interest can result in a higher interest earned over time, as the interest earned is added to the principal amount, and then the interest rate is applied to the new principal amount.

Q: How can 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, you can use the formula:

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

where:

• $A$ is the amount of money after $t$ years
• $P$ is the principal amount
• $r$ is the interest rate
• $t$ is the time period

The interest earned can be calculated by subtracting the principal amount from the amount of money after $t$ years.

Q: What is the difference between annual percentage rate (APR) and annual percentage yield (APY)?

A: Annual percentage rate (APR) is the interest rate charged on a loan or credit card, while annual percentage yield (APY) is the interest rate earned on a savings account or investment. APY takes into account the compounding of interest, while APR does not.

Q: How can I calculate the interest earned on a savings account with a variable interest rate?

A: To calculate the interest earned on a savings account with a variable interest rate, you can use the formula:

$$i = prt$$

where:

• $i$ is the interest earned
• $p$ is the principal amount
• $r$ is the interest rate (which can change over time)
• $t$ is the time period

You will need to use the current interest rate to calculate the interest earned, and then repeat the calculation as the interest rate changes.

Q: What is the impact of inflation on interest earned?

A: Inflation can reduce the purchasing power of the interest earned, as the interest earned is not adjusted for inflation. This means that the interest earned may not keep pace with the rising cost of living.

Q: How can I minimize the impact of inflation on interest earned?

A: To minimize the impact of inflation on interest earned, you can:

• Invest in assets that historically perform well during periods of inflation, such as precious metals or real estate
• Consider investing in a diversified portfolio of assets to reduce the impact of inflation on any one asset
• Review and adjust your investment strategy regularly to ensure that it remains aligned with your goals and risk tolerance

Q: What is the role of taxes in interest earned?

A: Taxes can reduce the interest earned on a savings account or investment. The tax rate will depend on the type of account or investment, as well as the individual's tax status.

Q: How can I minimize the impact of taxes on interest earned?

A: To minimize the impact of taxes on interest earned, you can:

• Consider investing in tax-deferred accounts, such as 401(k) or IRA accounts
• Review and adjust your investment strategy regularly to ensure that it remains aligned with your goals and risk tolerance
• Consider consulting with a tax professional to ensure that you are taking advantage of all available tax savings opportunities.