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)

Answer 1

To calculate the amount of interest earned on a principal amount deposited into an account with compound interest, you can use the formula for compound interest:

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

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.

In your case:
- \(P = 675\)
- \(r = 0.03\) (3% as a decimal)
- \(n = 4\) (compounded quarterly)
- \(t = 6\)

Let's plug in the values into the formula:

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

Calculating each part:

1. Calculate \( \frac{r}{n} \):
\[
\frac{0.03}{4} = 0.0075
\]

2. Calculate \( nt \):
\[
4 \times 6 = 24
\]

3. Now substitute back into the formula:
\[
A = 675 \left(1 + 0.0075\right)^{24}
\]
\[
A = 675 \left(1.0075\right)^{24}
\]

4. Calculate \( (1.0075)^{24} \):
\[
(1.0075)^{24} \approx 1.19668 \text{ (approximately)}
\]

5. Now calculate \( A \):
\[
A \approx 675 \times 1.19668 \approx 807.0
\]

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

\[
\text{Interest} = A - P = 807.0 - 675 = 132.0
\]

Thus, the interest earned after 6 years is approximately **$132.00**.