If $2000 is invested at an interest rate of 4.5% per year, compounded continuously, find the value of the investment after the given number of years. (Round your answers to the nearest cent.) a) 2 years b) 4 years c) 12 years

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If $2000 is invested at an interest rate of 4.5% per year, compounded continuously, find the value of the investment after the given number of years. (Round your answers to the nearest cent.) a) 2 years  b) 4 years c) 12 years

jlo2niT · Accepted Answer

Analyze the information provided. Due to the ongoing compounding of interest, the principal will grow tremendously. The amount after t years is given by&amp;nbsp;A(t)=Pert&amp;nbsp;It is given that the initial investment,P=$2000&amp;nbsp;and the interest rate per year,r=4.5%=0.045&amp;nbsp;Process: To determine the value of Amount after a specified number of years, enter the appropriate values for P, r, and t in each section a), b), and c. We must round replies to two decimals in order to round to the closest cent. a) After two years i.e t=2&amp;nbsp;A(t)=PertAfter two years: t=2&amp;nbsp;A(2)=2000e0.045(2)&amp;nbsp;A(2)=2000e0.09&amp;nbsp;A(2)=$2188.35&amp;nbsp;[rounded to two decimals(nearest cent) ] Amount after 2 years is $2188.35 b) After two years i.e t=4&amp;nbsp;A(t)=Pert&amp;nbsp;After two years: t=4&amp;nbsp;A(4)=2000e0.045(4)&amp;nbsp;A(4)=2000e0.18&amp;nbsp;A(4)=$2394.43&amp;nbsp;[rounded to two decimals(nearest cent) ] Amount after 4 years is $2394.43 c) After twelve years i.e t=12&amp;nbsp;A(t)=Pert&amp;nbsp;After two years: t=12&amp;nbsp;A(12)=2000e0.045(12)&amp;nbsp;A(12)=2000e0.54&amp;nbsp;A(12)=$3432.01&amp;nbsp;[rounded to two decimals(nearest cent)] Amount after 12 years is $3432.01

If $2000 is invested at an interest rate of 4.5% per year, compounded continuously, find the value of the investment after the given number of years. (Round your answers to the nearest cent.) a) 2 years b) 4 years c) 12 years

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