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

$807.58
$807.58

$121.50
$121.50

$130.99
$130.99

$132.58

Answer 1

To calculate the total amount and interest earned on a principal amount with compound interest, you 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:
- \( P = 675 \)
- \( r = 0.03 \) (3% expressed as a decimal)
- \( n = 4 \) (compounded quarterly)
- \( t = 6 \)

Now plugging in the values:

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

First, calculate \( \frac{0.03}{4} \):

\[
\frac{0.03}{4} = 0.0075
\]

Now substitute back into the formula:

\[
A = 675 \left(1 + 0.0075\right)^{24}
\]
\[
A = 675 \left(1.0075\right)^{24}
\]

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

\[
(1.0075)^{24} \approx 1.191505
\]

Now calculate \( A \):

\[
A \approx 675 \times 1.191505 \approx 803.26
\]

To find the interest earned, subtract the principal from the total amount:

\[
\text{Interest} = A - P = 803.26 - 675 \approx 128.26
\]

The closest option provided is:

- **$130.99**

Therefore, the correct answer is approximately **$130.99**.