Question: Dolores invests $8100 in a new savings account which earns 3.0% annual interest, compounded…

Dolores invests $8100 in a new savings account which earns 3.0% annual interest, compounded quarterly. What will be the value of her investment after 3 years? Round to the nearest cent.

Answer

Solution

Dolores invests $8100 in a new savings account which earns 3.0% annual interest, compounded quarterly. To find out the value of her investment after 3 years, we 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 (\$8100). - \( r \) is the annual interest rate (3.0% or 0.03). - \( n \) is the number of times that interest is compounded per year (quarterly means \( n = 4 \)). - \( t \) is the number of years the money is invested for (3 years). Plug in the values: \[ A = 8100 \left(1 + \frac{0.03}{4}\right)^{4 \times 3} \] Calculate the interest rate per quarter: \[ \frac{0.03}{4} = 0.0075 \] Calculate the number of compounding periods: \[ 4 \times 3 = 12 \] Substitute these values into the formula: \[ A = 8100 \left(1 + 0.0075\right)^{12} \] Simplify inside the parentheses: \[ A = 8100 \times \left(1.0075\right)^{12} \] Calculate the power: \[ 1.0075^{12} \approx 1.093443 \] Calculate the final amount: \[ A = 8100 \times 1.093443 \approx 8856.89 \] Therefore, the value of her investment after 3 years is approximately \$8856.89.