Question

About how much interest will be earned on a principal of $675 deposited into account paying 3% interest compound quarterly which is four times per year for 6 years

Answer 1

To calculate the interest earned on a principal amount compounded quarterly, we 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 time in years.

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

Substituting these values into the formula gives:

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

Calculating the values step-by-step:

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

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

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

4. Calculate \( (1.0075)^{24} \):
\[
(1.0075)^{24} \approx 1.194052
\]

5. Now calculate \( A \):
\[
A \approx 675 \times 1.194052 \approx 805.24
\]

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

\[
\text{Interest} = A - P = 805.24 - 675 = 130.24
\]

So, the interest earned over 6 years is approximately **$130.24**.