Answer :
To solve the problem, we need to calculate the balance of a savings account after applying the Annual Percentage Yield (APY). The APY is given as 3.9%, and the principal amount is [tex]$3700.
Here's a step-by-step guide to finding the solution:
1. Understand APY: The APY is the effective annual rate of return taking into account the effect of compounding interest. Since it's calculated for a year, we only need to find how much interest $[/tex]3700 earns at a 3.9% rate over one year.
2. Convert APY to a Decimal: To use the rate in calculations, convert the percentage to a decimal. So, 3.9% becomes 0.039 (because 3.9 divided by 100 equals 0.039).
3. Calculate Interest Earned: Multiply the principal amount by the converted APY to find the interest earned in one year.
[tex]\[
\text{Interest Earned} = \text{Principal} \times \text{APY} = 3700 \times 0.039 = 144.30
\][/tex]
4. Calculate the Final Balance: Add the interest earned to the principal to get the new balance after one year.
[tex]\[
\text{Balance} = \text{Principal} + \text{Interest Earned} = 3700 + 144.30 = 3844.30
\][/tex]
Therefore, the balance of the savings account after one year will be [tex]$3844.30.
The correct answer is D. $[/tex]3844.30.
Here's a step-by-step guide to finding the solution:
1. Understand APY: The APY is the effective annual rate of return taking into account the effect of compounding interest. Since it's calculated for a year, we only need to find how much interest $[/tex]3700 earns at a 3.9% rate over one year.
2. Convert APY to a Decimal: To use the rate in calculations, convert the percentage to a decimal. So, 3.9% becomes 0.039 (because 3.9 divided by 100 equals 0.039).
3. Calculate Interest Earned: Multiply the principal amount by the converted APY to find the interest earned in one year.
[tex]\[
\text{Interest Earned} = \text{Principal} \times \text{APY} = 3700 \times 0.039 = 144.30
\][/tex]
4. Calculate the Final Balance: Add the interest earned to the principal to get the new balance after one year.
[tex]\[
\text{Balance} = \text{Principal} + \text{Interest Earned} = 3700 + 144.30 = 3844.30
\][/tex]
Therefore, the balance of the savings account after one year will be [tex]$3844.30.
The correct answer is D. $[/tex]3844.30.
