Question: Question 2 of 12, Step 1 of 1 Tessa invests $5600 in a new savings account which earns 4.0% annual…

Question 2 of 12, Step 1 of 1

Tessa invests $5600 in a new savings account which earns 4.0% annual interest, compounded semi-annually. What will be the value of her investment after 8 years? Round to the nearest cent.

Answer

How to enter your answer (opens in new window)

$

Solution

Tessa invests $5600 in a new savings account which earns 4.0% annual interest, compounded semi-annually. We need to find the value of her investment after 8 years and round it to the nearest cent. The formula for compound interest is: \[ A = P \left(1 + \frac{r}{n}\right)^{nt} \] where: - \(A\) is the amount of money accumulated after n years, including interest. - \(P\) is the principal amount ($5600). - \(r\) is the annual interest rate (decimal) (0.04). - \(n\) is the number of times that interest is compounded per year (2 for semi-annually). - \(t\) is the number of years the money is invested for (8). Substitute the given values into the formula: \[ A = 5600 \left(1 + \frac{0.04}{2}\right)^{2 \times 8} \] Calculate the interest rate per period: \[ \frac{0.04}{2} = 0.02 \] Now calculate the number of compounding periods: \[ 2 \times 8 = 16 \] Substitute these into the equation: \[ A = 5600 \left(1 + 0.02\right)^{16} \] Calculate \(1 + 0.02\): \[ 1 + 0.02 = 1.02 \] Raise \(1.02\) to the power of 16: \[ 1.02^{16} \approx 1.3728 \] Multiply by the principal: \[ A = 5600 \times 1.3728 \approx 7687.68 \] Therefore, the value of her investment after 8 years is approximately $7687.68.