Question

About how much interest will be earned on a principal of $675 deposited into an account paying 3% interest compounded quarterly (4 times per year) for 6 years?(1 point)
Responses

$130.99
$130.99

$132.58
$132.58

$807.58
$807.58

$121.50

Answer 1

To calculate the amount of interest earned on a principal amount with compound interest, we can use the 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 number of years the money is invested or borrowed.

**Given:**
- Principal \( P = 675 \)
- Annual interest rate \( r = 3\% = 0.03 \)
- Compounded quarterly, so \( n = 4 \)
- Time period \( t = 6 \) years

Now plug these values into the formula:

\[
A = 675 \left(1 + \frac{0.03}{4}\right)^{4 \times 6}
\]
\[
A = 675 \left(1 + 0.0075\right)^{24}
\]
\[
A = 675 \left(1.0075\right)^{24}
\]

Now calculate \( (1.0075)^{24} \):

\[
(1.0075)^{24} \approx 1.19786
\]

Now, plug this back into the equation for \( A \):

\[
A \approx 675 \times 1.19786 \approx 808.14
\]

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

\[
\text{Interest} = A - P = 808.14 - 675 = 133.14
\]

Thus, the approximate interest earned is about **$133.14**. Since that isn't exactly one of the options provided, the closest response would be **$132.58**.

So the answer is:

**$132.58**