The compound interest formula is given by \[ A=P\left(1+\frac{r}{n}\right)^{n t} \] where \( A \) is the accumulated amount, after an initial investment of \( P \) dollars is invested for \( t \) years, at annual interest rate \( r \), compounded \( n \) times per year. Use the formula above to determine how long it will take an initial investment of \( \$ 14,250 \) to grow to \( \$ 65,550 \), if the account earns \( 14.92 \% \) interest per year, compounded annually. Round the solution to two decimal places. The account balance will reach \( \$ 65,550 \) after years.
The continuous compound interest formula is given by \[ A=P e^{r t} \] where \( A \) is the accumulated amount, after an initial investment of \( P \) dollars is invested for \( t \) years, at annual interest rate \( r \), compounded continuously. Use the formula above to determine the accumulated amount for each of the following different scenarios. Round solutions to the nearest cent. If \( \$ 25,000 \) is invested for 17 years and earns \( 12.5 \% \) interest, compounded continuously, the accumulated amount is: \[ A= \] If \( \$ 36,000 \) is invested for 12 years and earns \( 8.5 \% \) interest, compounded continuously, the accumulated amount is: \[ A= \] If \( \$ 45,000 \) is invested for 19 years and earns \( 4.5 \% \) interest, compounded continuously, the accumulated amount is: \[ A= \] If \( \$ 35,000 \) is invested for 27 years and earns \( 10.5 \% \) interest, compounded continuously, the accumulated amount is:
The compound interest formula is given by \[ A=P\left(1+\frac{r}{n}\right)^{n t} \] where \( A \) is the accumulated amount, after an initial investment of \( P \) dollars is invested for \( t \) years, at annual interest rate \( r \), compounded \( n \) times per year. Use the formula above to determine how long it will take an initial investment of \( \$ 9,750 \) to grow to \( \$ 20,475 \), if the account earns \( 6.7 \% \) interest per year, compounded annually. Round the solution to two decimal places. The account balance will reach \( \$ 20,475 \) after years.
The population of Stuart can be modeled by the function \[ P=16429 e^{0.002796 t} \] where \( t \) is the number of years since 2020 . Use the above function to answer the following questions. What was the population of Stuart in 2020? In what year is the population of Stuart projected to reach 24,644 ? Round the solution to the nearest whole number.