John has a bank account with \( \$ 7,362 \). He decides to invest the money at \( 4.85 \% \) interest, compounded annually. How much will the investment be worth after 9 years? Round to the nearest dollar. Type your numerical answer below.
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To calculate the future value of John's investment, 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. - \( P \) is the principal amount (the initial money, which is \( 7362 \)). - \( r \) is the annual interest rate (decimal) (which is \( 0.0485 \)). - \( t \) is the number of years the money is invested (which is \( 9 \)). Plugging in the values: \[ A = 7362(1 + 0.0485)^9 \] \[ A = 7362(1.0485)^9 \] \[ A = 7362 \times 1.488864 \] \[ A \approx 10906.64 \] Rounding to the nearest dollar, the investment will be worth approximately \( \$ 10,907 \) after 9 years.