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Find the value after five years of a $3,000 savings account that pays 3% interest compounded yearly. Round the answer to two de...Asked by Correct Answers!
Find the value after five years of a $3,000 savings account that pays 3% interest compounded yearly. Round the answer to two decimal places.(1 point)
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explain
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i dont understand
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how do you do the equation
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GPT 3.5
The formula to calculate the future value of an investment with compound interest is given by:
A = P(1 + r/n)^(n*t)
Where:
A = future value
P = principal amount (initial investment)
r = annual interest rate (as a decimal)
n = number of times the interest is compounded per year
t = number of years
In this case, P = $3,000, r = 0.03 (3% expressed as a decimal), n = 1 (compounded yearly), and t = 5 years.
Plugging in the values, we have:
A = 3000(1 + 0.03/1)^(1*5)
A ≈ 3000(1 + 0.03)^(5)
A ≈ 3000(1.03)^(5)
A ≈ 3000(1.1592740743)
A ≈ 3477.82
Therefore, the value after five years of a $3,000 savings account that pays 3% interest compounded yearly is approximately $3,477.82.
A = P(1 + r/n)^(n*t)
Where:
A = future value
P = principal amount (initial investment)
r = annual interest rate (as a decimal)
n = number of times the interest is compounded per year
t = number of years
In this case, P = $3,000, r = 0.03 (3% expressed as a decimal), n = 1 (compounded yearly), and t = 5 years.
Plugging in the values, we have:
A = 3000(1 + 0.03/1)^(1*5)
A ≈ 3000(1 + 0.03)^(5)
A ≈ 3000(1.03)^(5)
A ≈ 3000(1.1592740743)
A ≈ 3477.82
Therefore, the value after five years of a $3,000 savings account that pays 3% interest compounded yearly is approximately $3,477.82.
Answered by
GPT 3.5
Sure!
Compound interest is when interest is calculated on both the initial amount of money (called the principal amount) and any accumulated interest. In this case, we have a savings account with a principal amount of $3,000 and an annual interest rate of 3%. The interest is compounded yearly, meaning it is calculated once a year.
To find the future value of this investment after five years, we can use the formula A = P(1 + r/n)^(n*t), where A represents the future value, P represents the principal amount, r represents the annual interest rate, n represents the number of times the interest is compounded per year, and t represents the number of years.
By plugging in the given values, we have A = 3000(1 + 0.03/1)^(1*5). We simplify this to A ≈ 3000(1 + 0.03)^(5). To further calculate, we use the value 1.03 (1 + 0.03) raised to the power of 5, resulting in 1.03^5 ≈ 1.1592740743.
Finally, we multiply the principal amount, $3,000, by the calculated value to find the future value. A ≈ 3000(1.1592740743) ≈ 3477.82.
Hence, after five years, the savings account will have a value of approximately $3,477.82.
Compound interest is when interest is calculated on both the initial amount of money (called the principal amount) and any accumulated interest. In this case, we have a savings account with a principal amount of $3,000 and an annual interest rate of 3%. The interest is compounded yearly, meaning it is calculated once a year.
To find the future value of this investment after five years, we can use the formula A = P(1 + r/n)^(n*t), where A represents the future value, P represents the principal amount, r represents the annual interest rate, n represents the number of times the interest is compounded per year, and t represents the number of years.
By plugging in the given values, we have A = 3000(1 + 0.03/1)^(1*5). We simplify this to A ≈ 3000(1 + 0.03)^(5). To further calculate, we use the value 1.03 (1 + 0.03) raised to the power of 5, resulting in 1.03^5 ≈ 1.1592740743.
Finally, we multiply the principal amount, $3,000, by the calculated value to find the future value. A ≈ 3000(1.1592740743) ≈ 3477.82.
Hence, after five years, the savings account will have a value of approximately $3,477.82.
Answered by
GPT 3.5
I apologize for any confusion. Let me explain the process in simpler terms.
We have a savings account with $3,000 initial deposit. The account pays 3% interest per year, which means that each year, the amount of money in the account increases by 3% of its current value.
After one year, the account would have the initial deposit of $3,000 plus 3% of $3,000, which is $90. This means the total amount in the account after one year would be $3,000 + $90 = $3,090.
To find the amount after five years, we need to repeat this calculation five times.
After the second year, the amount would be the previous amount of $3,090 plus 3% of $3,090. This gives us $3,090 + 3% of $3,090, which is $93.30. So, after the second year, the total amount in the account would be $3,090 + $93.30 = $3,183.30.
Similarly, after the third year, the amount would be the previous amount of $3,183.30 plus 3% of $3,183.30. After the fourth year, we would add 3% of the previous amount, and after the fifth year, we would add 3% of the previous amount again.
To simplify this calculation, we can use the formula for compound interest, which is A = P(1 + r/n)^(n*t), as mentioned before. By plugging in the values, we find that after five years, the total amount in the account would be approximately $3,477.82.
I hope this explanation is clearer.
We have a savings account with $3,000 initial deposit. The account pays 3% interest per year, which means that each year, the amount of money in the account increases by 3% of its current value.
After one year, the account would have the initial deposit of $3,000 plus 3% of $3,000, which is $90. This means the total amount in the account after one year would be $3,000 + $90 = $3,090.
To find the amount after five years, we need to repeat this calculation five times.
After the second year, the amount would be the previous amount of $3,090 plus 3% of $3,090. This gives us $3,090 + 3% of $3,090, which is $93.30. So, after the second year, the total amount in the account would be $3,090 + $93.30 = $3,183.30.
Similarly, after the third year, the amount would be the previous amount of $3,183.30 plus 3% of $3,183.30. After the fourth year, we would add 3% of the previous amount, and after the fifth year, we would add 3% of the previous amount again.
To simplify this calculation, we can use the formula for compound interest, which is A = P(1 + r/n)^(n*t), as mentioned before. By plugging in the values, we find that after five years, the total amount in the account would be approximately $3,477.82.
I hope this explanation is clearer.
Answered by
GPT 3.5
To calculate the future value using the compound interest formula A = P(1 + r/n)^(n*t), follow these steps:
1. Identify the values:
- P = principal amount (initial deposit) = $3,000
- r = annual interest rate (as a decimal) = 0.03
- n = number of times the interest is compounded per year (compounded yearly in this case) = 1
- t = number of years = 5
2. Plug in the values into the formula:
A = 3000(1 + 0.03/1)^(1*5)
3. Simplify the expression within the parentheses:
A = 3000(1 + 0.03)^(5)
4. Calculate the value of (1 + 0.03) raised to the power of 5, which is (1.03)^5 = 1.1592740743 (rounding it to 10 decimal places).
5. Now substitute this value back into the formula:
A ≈ 3000 * 1.1592740743
6. Multiply the principal amount ($3,000) by the value obtained to find the future value:
A ≈ 3000 * 1.1592740743 ≈ 3477.82222222
7. Round the answer to two decimal places, as requested:
A ≈ $3,477.82
Therefore, after five years, the value of the savings account will be approximately $3,477.82.
1. Identify the values:
- P = principal amount (initial deposit) = $3,000
- r = annual interest rate (as a decimal) = 0.03
- n = number of times the interest is compounded per year (compounded yearly in this case) = 1
- t = number of years = 5
2. Plug in the values into the formula:
A = 3000(1 + 0.03/1)^(1*5)
3. Simplify the expression within the parentheses:
A = 3000(1 + 0.03)^(5)
4. Calculate the value of (1 + 0.03) raised to the power of 5, which is (1.03)^5 = 1.1592740743 (rounding it to 10 decimal places).
5. Now substitute this value back into the formula:
A ≈ 3000 * 1.1592740743
6. Multiply the principal amount ($3,000) by the value obtained to find the future value:
A ≈ 3000 * 1.1592740743 ≈ 3477.82222222
7. Round the answer to two decimal places, as requested:
A ≈ $3,477.82
Therefore, after five years, the value of the savings account will be approximately $3,477.82.
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