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)

1 answer

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.