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

ddaeeric 2020-12-02 Answered
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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jlo2niT
Answered 2020-12-03 Author has 96 answers
Analyse the given information Since the interest is compounded continuously, the Principal will increase exponentially. The amount after t years is given by A(t)=Pert It is given that the initial investment,P=$2000 and the interest rate per year,r=4.5%=0.045 Process: In each part a), b) and c) plug in values of P, r and t in each case to find the value of Amount after a given number of years. To round to nearest cent we need to round answers to two decimals. a) After two years i.e t=2 A(t)=Pert After two years: t=2 A(2)=2000e0.045(2)
A(2)=2000e0.09
A(2)=$2188.35 [rounded to two decimals(nearest cent) ] Amount after 2 years is $2188.35 b) After two years i.e t=4 A(t)=Pert After two years: t=4 A(4)=2000e0.045(4)
A(4)=2000e0.18
A(4)=$2394.43 [rounded to two decimals(nearest cent) ] Amount after 4 years is $2394.43 c) After twelve years i.e t=12 A(t)=Pert After two years: t=12 A(12)=2000e0.045(12)
A(12)=2000e0.54
A(12)=$3432.01 [rounded to two decimals(nearest cent)] Amount after 12 years is $3432.01
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