Formula 1 point You need to have saved \( \$ 877 \) exactly 7 years from today. If you deposit \( \$ 442 \) in an account today, what is the annual interest rate must you earn? Enter your answer as a decimal, and show 4 decimal places. For example, if your answer is \( 6.5 \% \), you should enter. 0650 . Type your answer_

To find the annual interest rate needed to turn $442 into $877 over 7 years, we can use the formula for compound interest: \[ A = P(1 + r)^t \] where: - \( A \) is the amount of money accumulated after n years, including interest (in this case, $877), - \( P \) is the principal amount (the initial deposit or investment, here $442), - \( r \) is the annual interest rate (in decimal), - \( t \) is the number of years the money is invested or borrowed (which is 7 years). Rearranging the formula to solve for \( r \): \[ 877 = 442(1 + r)^7 \] Dividing both sides by 442 gives: \[ \frac{877}{442} = (1 + r)^7 \] Calculating \( \frac{877}{442} \): \[ \frac{877}{442} \approx 1.9842 \] Now taking the 7th root of both sides: \[ 1 + r = (1.9842)^{\frac{1}{7}} \] Calculating the 7th root: \[ 1 + r \approx 1.2662 \] Thus: \[ r \approx 1.2662 - 1 = 0.2662 \] Therefore, the interest rate \( r \) is approximately \( 0.2662 \) in decimal form. Please enter 0.2662 for your answer.