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Answer :
To find the balance of a savings account after a year with an annual percentage yield (APY) of 3.9%, follow these steps:
1. Understand the Terms:
- Principal: This is the initial amount placed in the savings account. Here, it's [tex]$3700.
- APY (Annual Percentage Yield): This represents the annual interest rate, accounting for the effect of compounding. In this problem, the APY is 3.9%.
2. Convert APY to Decimal:
- Since percentages are easier to work with when converted to decimals, convert 3.9% to a decimal by dividing by 100.
- \( \text{Annual Interest Rate} = \frac{3.9}{100} = 0.039 \).
3. Calculate the Final Balance:
- To find the balance after one year, add the interest to the principal. This can be calculated as the original principal amount multiplied by (1 plus the interest rate in decimal form).
- \( \text{Final Balance} = \text{Principal} \times (1 + \text{Annual Interest Rate}) \).
- Plugging in the numbers:
- \( \text{Final Balance} = 3700 \times (1 + 0.039) = 3700 \times 1.039 \).
4. Compute the Result:
- Performing the multiplication gives the final balance:
- \( 3700 \times 1.039 = 3844.30 \).
So, the balance of the savings account after one year will be approximately $[/tex]3844.30. Therefore, the correct answer is B. $3844.30.
1. Understand the Terms:
- Principal: This is the initial amount placed in the savings account. Here, it's [tex]$3700.
- APY (Annual Percentage Yield): This represents the annual interest rate, accounting for the effect of compounding. In this problem, the APY is 3.9%.
2. Convert APY to Decimal:
- Since percentages are easier to work with when converted to decimals, convert 3.9% to a decimal by dividing by 100.
- \( \text{Annual Interest Rate} = \frac{3.9}{100} = 0.039 \).
3. Calculate the Final Balance:
- To find the balance after one year, add the interest to the principal. This can be calculated as the original principal amount multiplied by (1 plus the interest rate in decimal form).
- \( \text{Final Balance} = \text{Principal} \times (1 + \text{Annual Interest Rate}) \).
- Plugging in the numbers:
- \( \text{Final Balance} = 3700 \times (1 + 0.039) = 3700 \times 1.039 \).
4. Compute the Result:
- Performing the multiplication gives the final balance:
- \( 3700 \times 1.039 = 3844.30 \).
So, the balance of the savings account after one year will be approximately $[/tex]3844.30. Therefore, the correct answer is B. $3844.30.
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