If the APY of a savings account is 3.9%, and the principal in the savings account is [tex]$3700[/tex] for an entire year, what will be the balance of the savings account after all the interest is paid for the year?

A. [tex]$3714.43[/tex]
B. [tex]$3700.00[/tex]
C. [tex]$3900.00[/tex]
D. [tex]$3844.30[/tex]

Sure! Let's work through the problem step by step.

To find out the balance of the savings account after a year with an APY (Annual Percentage Yield) of 3.9%, follow these steps:

1. Understand the Terms:
- Principal: This is the initial amount of money in the savings account, which is [tex]$3,700.
- APY (Annual Percentage Yield): This is the annual interest rate, which is 3.9%. The APY represents the total return on an account, including the effect of compounding interest.

2. Calculate the Interest Earned:
To find out how much interest the account earns in a year, multiply the principal by the APY (expressed as a decimal).

\[
\text{Interest Earned} = \text{Principal} \times \left(\frac{\text{APY}}{100}\right)
\]

Plug in the values:

\[
\text{Interest Earned} = 3700 \times 0.039
\]

\[
\text{Interest Earned} = 144.3
\]

So, the interest earned after a year is $[/tex]144.30.

3. Calculate the New Balance:
Add the interest earned to the principal to find the new balance.

[tex]\[
\text{Balance} = \text{Principal} + \text{Interest Earned}
\][/tex]

[tex]\[
\text{Balance} = 3700 + 144.3
\][/tex]

[tex]\[
\text{Balance} = 3844.3
\][/tex]

Therefore, the balance of the savings account after one year will be [tex]$3,844.30.

From the given options, the correct answer is D. $[/tex]3844.30.