Respuesta :
Given:
In January Joanna deposited $250 into her savings account.
In February, she deposited an additional $100.
Her account has an APR of 6% compounded monthly.
Required:
We have to find how much interest did Joanna earn in the first two months.
Explanation:
For the month of January:
[tex]A=P(1+\frac{r}{100})^n[/tex]Here, P=$250, r=6%, amd n= 1 month=1/12 year.
Then,
[tex]\begin{gathered} A=250(1+\frac{6}{100})^{\frac{1}{12}} \\ \\ A=250(\frac{106}{100})^{\frac{1}{12}} \end{gathered}[/tex][tex]\begin{gathered} A=250\times1.005 \\ A=\text{ \$}251.25 \end{gathered}[/tex]Then the interest is
[tex]I=A-P=251.25-250=\text{ \$}1.25[/tex]For the month of February:
P=251.24+100=351.25
Then we have
[tex]\begin{gathered} A=351.25(1+\frac{6}{100})^{\frac{1}{12}} \\ \\ A=351.25(\frac{106}{100})^{\frac{1}{12}} \end{gathered}[/tex][tex]\begin{gathered} A=351.5\times1.005 \\ A=\text{ \$}353.01 \end{gathered}[/tex]Then the interest is
[tex]A=P-I=353.01-351.25=\text{ \$}1.76[/tex]Therefore, the total interest is
[tex]1.25+1.76=\text{ \$}3.01[/tex]Final answer:
Hence the final answer is
[tex]\text{ \$}3.01[/tex]
