you consistently deposit $250.00 into a savings account on the 15th of each month, and the account earns a…

Explanation:

Step1: Calculate the monthly - interest rate

The annual percentage rate (APR) is 2.5% or 0.025 in decimal form. The monthly - interest rate $r$ is $\frac{0.025}{12}$.

Step2: Analyze the first deposit

The first deposit of $250$ is made on the 15th of the first month. By the end of the third month, it will earn interest for 2.5 months. The future - value of the first deposit $FV_1$ is $250(1 + r)^{2.5}$, where $r=\frac{0.025}{12}$.

Step3: Analyze the second deposit

The second deposit of $250$ is made on the 15th of the second month. By the end of the third month, it will earn interest for 1.5 months. The future - value of the second deposit $FV_2$ is $250(1 + r)^{1.5}$.

Step4: Analyze the third deposit

The third deposit of $250$ is made on the 15th of the third month. By the end of the third month, it will earn interest for 0.5 months. The future - value of the third deposit $FV_3$ is $250(1 + r)^{0.5}$.

Step5: Calculate the total balance

The total balance $B$ of the savings account at the end of the third full month is $B = 250(1+\frac{0.025}{12})^{2.5}+250(1 + \frac{0.025}{12})^{1.5}+250(1+\frac{0.025}{12})^{0.5}$.

First, calculate $(1+\frac{0.025}{12})\approx1.0020833$.

$FV_1=250\times(1.0020833)^{2.5}\approx250\times1.00521=251.3025$.

$FV_2=250\times(1.0020833)^{1.5}\approx250\times1.00312=250.78$.

$FV_3=250\times(1.0020833)^{0.5}\approx250\times1.00104=250.26$.

$B=251.3025 + 250.78+250.26=752.3425\approx752.34$.

Answer:

$752.34$