Question

Round any decimals to the nearest penny. You save $3,260.00 in a savings account earning 3.55% APR compounded monthly.
How much is the total interest earned by the end of the third month?

Answer 1

To calculate the total interest earned by the end of the third month in a savings account with an APR of 3.55% compounded monthly, we can use the compound interest formula:

\[
A = P \left(1 + \frac{r}{n}\right)^{nt}
\]

Where:
- \(A\) is the amount of money accumulated after n years, including interest.
- \(P\) is the principal amount (the initial amount of money).
- \(r\) is the annual interest rate (decimal).
- \(n\) is the number of times that interest is compounded per year.
- \(t\) is the time the money is invested or borrowed for in years.

Given:
- \(P = 3260.00\)
- \(r = 3.55\% = 0.0355\)
- \(n = 12\) (since it's compounded monthly)
- \(t = \frac{3}{12} = 0.25\) years (for 3 months)

Now, substituting these values into the formula:

\[
A = 3260 \left(1 + \frac{0.0355}{12}\right)^{12 \cdot 0.25}
\]

Calculating \(\frac{0.0355}{12}\):

\[
\frac{0.0355}{12} \approx 0.00295833
\]

Now calculate \(A\):

\[
A = 3260 \left(1 + 0.00295833\right)^{3}
\]

Calculating \((1 + 0.00295833)^3\):

\[
(1.00295833)^3 \approx 1.008895
\]

Now, substituting this back into the formula for \(A\):

\[
A \approx 3260 \times 1.008895 \approx 3284.06
\]

Now, to find the interest earned, subtract the initial principal from the total amount:

\[
\text{Interest} = A - P = 3284.06 - 3260.00 = 24.06
\]

Thus, the total interest earned by the end of the third month, rounded to the nearest penny, is **$24.06**.