Answer:
$29.02.
Step-by-step explanation:
We have been given that you save 3 ,260.00 in a savings account earning a 3.55% APR compounded monthly. We are asked to find the total interest earned by the end of the third month.
We will use compound interest formula to solve our given problem.
[tex]A=P(1+\frac{r}{n})^{nt}[/tex], where,
A = Amount of interest after t years,
P = Principal amount,
r = Annual interest rate in decimal form,
n = Number of periods interest is compounded per year,
t = Time in years.
[tex]3.55\%=\frac{3.55}{100}=0.0355[/tex]
[tex]\text{3 months}=\frac{3}{12}\text{ year}=\frac{1}{4}\text{ year}[/tex]
Upon substituting our given values in above formula, we will get:
[tex]A=3,260(1+\frac{0.0355}{12})^{12\times \frac{1}{4}}[/tex]
[tex]A=3,260(1+0.002958333)^{3}[/tex]
[tex]A=3,260(1.002958333)^{3}[/tex]
[tex]A=3,260*1.00890128109888[/tex]
[tex]A=3289.0181763823\approx 3289.02[/tex]
Now, we will subtract principal amount from final amount to find amount of interest.
[tex]\text{Amount of interest}=3289.02-3260[/tex]
[tex]\text{Amount of interest}=29.02[/tex]
Therefore, you will earn am amount of $29.02 by the end of the third month.
