Meg Has $$ 90 , 000 90,000 90 , 000 $ In A Savings Account. The Interest Rate Is $1 \frac{4}{5} %$ Per Year And Is Not Compounded. How Much Will She Have In Total In 1 Year? Use The Formula $i = P \cdot R \cdot T$, Where
Meg's Savings Account and the Interest Rate
Meg has a savings account with a balance of $90,000. The interest rate on this account is 1 and 4/5 percent per year, which can be expressed as a decimal by dividing the numerator by the denominator and then dividing by 100. To find the decimal equivalent of 1 and 4/5 percent, we divide 4 by 5 and then divide the result by 100, which gives us 0.8/100 = 0.008. Therefore, the interest rate is 1.008 percent.
The Formula for Simple Interest
The formula for simple interest is given by the equation i = p * r * t, where i is the interest earned, p is the principal amount (initial investment), r is the interest rate, and t is the time period in years. In this case, the principal amount is $90,000, the interest rate is 1.008 percent, and the time period is 1 year.
Applying the Formula to Meg's Savings Account
To find the interest earned on Meg's savings account, we can plug in the values into the formula i = p * r * t. The principal amount p is $90,000, the interest rate r is 0.008, and the time period t is 1 year. Substituting these values into the formula, we get:
i = 90,000 * 0.008 * 1 i = 720
Calculating the Total Amount in the Savings Account
To find the total amount in the savings account after 1 year, we need to add the interest earned to the principal amount. The interest earned is $720, and the principal amount is $90,000. Therefore, the total amount in the savings account after 1 year is:
Total Amount = Principal Amount + Interest Earned Total Amount = $90,000 + $720 Total Amount = $90,720
Conclusion
In this problem, we used the formula for simple interest to calculate the interest earned on Meg's savings account. We then added the interest earned to the principal amount to find the total amount in the savings account after 1 year. The total amount in the savings account after 1 year is $90,720.
Key Takeaways
- The formula for simple interest is i = p * r * t, where i is the interest earned, p is the principal amount, r is the interest rate, and t is the time period in years.
- To find the interest earned, we need to multiply the principal amount by the interest rate and the time period.
- To find the total amount in the savings account, we need to add the interest earned to the principal amount.
Real-World Applications
The formula for simple interest has many real-world applications. For example, it can be used to calculate the interest earned on a savings account, a loan, or an investment. It can also be used to calculate the total amount owed on a loan or the total amount earned on an investment.
Example Problems
- A person has a savings account with a balance of $10,000. The interest rate on this account is 2 percent per year. How much will the person have in the account after 2 years?
- A person borrows $5,000 at an interest rate of 5 percent per year. How much will the person owe after 3 years?
Solutions to Example Problems
- To find the interest earned, we need to multiply the principal amount by the interest rate and the time period. The principal amount is $10,000, the interest rate is 0.02, and the time period is 2 years. Therefore, the interest earned is:
i = 10,000 * 0.02 * 2 i = 400
To find the total amount in the account after 2 years, we need to add the interest earned to the principal amount. The interest earned is $400, and the principal amount is $10,000. Therefore, the total amount in the account after 2 years is:
Total Amount = Principal Amount + Interest Earned Total Amount = $10,000 + $400 Total Amount = $10,400
- To find the interest earned, we need to multiply the principal amount by the interest rate and the time period. The principal amount is $5,000, the interest rate is 0.05, and the time period is 3 years. Therefore, the interest earned is:
i = 5,000 * 0.05 * 3 i = 750
To find the total amount owed after 3 years, we need to add the interest earned to the principal amount. The interest earned is $750, and the principal amount is $5,000. Therefore, the total amount owed after 3 years is:
Q: What is the formula for simple interest?
A: The formula for simple interest is i = p * r * t, where i is the interest earned, p is the principal amount, r is the interest rate, and t is the time period in years.
Q: How do I calculate the interest earned on a savings account?
A: To calculate the interest earned, you need to multiply the principal amount by the interest rate and the time period. For example, if the principal amount is $90,000, the interest rate is 1.008 percent, and the time period is 1 year, the interest earned would be:
i = 90,000 * 0.008 * 1 i = 720
Q: How do I calculate the total amount in a savings account after a certain period of time?
A: To calculate the total amount in a savings account after a certain period of time, you need to add the interest earned to the principal amount. For example, if the principal amount is $90,000 and the interest earned is $720, the total amount in the account after 1 year would be:
Total Amount = Principal Amount + Interest Earned Total Amount = $90,000 + $720 Total Amount = $90,720
Q: What is the difference between simple interest and compound interest?
A: Simple interest is calculated only on the 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 total amount over time.
Q: How do I calculate compound interest?
A: To calculate compound interest, you need to use the formula A = P(1 + r/n)^(nt), where A is the total amount, P is the principal amount, r is the interest rate, n is the number of times interest is compounded per year, and t is the time period in years.
Q: What is the interest rate on Meg's savings account?
A: The interest rate on Meg's savings account is 1 and 4/5 percent per year, which can be expressed as a decimal by dividing the numerator by the denominator and then dividing by 100. To find the decimal equivalent of 1 and 4/5 percent, we divide 4 by 5 and then divide the result by 100, which gives us 0.8/100 = 0.008. Therefore, the interest rate is 1.008 percent.
Q: How much will Meg have in her savings account after 1 year?
A: To find the total amount in Meg's savings account after 1 year, we need to add the interest earned to the principal amount. The interest earned is $720, and the principal amount is $90,000. Therefore, the total amount in the account after 1 year is:
Total Amount = Principal Amount + Interest Earned Total Amount = $90,000 + $720 Total Amount = $90,720
Q: What is the principal amount on Meg's savings account?
A: The principal amount on Meg's savings account is $90,000.
Q: What is the time period for the interest calculation on Meg's savings account?
A: The time period for the interest calculation on Meg's savings account is 1 year.
Q: What is the interest earned on Meg's savings account?
A: The interest earned on Meg's savings account is $720.
Q: How do I calculate the interest earned on a loan?
A: To calculate the interest earned on a loan, you need to multiply the principal amount by the interest rate and the time period. For example, if the principal amount is $5,000, the interest rate is 5 percent, and the time period is 3 years, the interest earned would be:
i = 5,000 * 0.05 * 3 i = 750
Q: How do I calculate the total amount owed on a loan?
A: To calculate the total amount owed on a loan, you need to add the interest earned to the principal amount. For example, if the principal amount is $5,000 and the interest earned is $750, the total amount owed would be:
Total Amount = Principal Amount + Interest Earned Total Amount = $5,000 + $750 Total Amount = $5,750