When interest is compounded continuously, the amount of money increases at a rate proportional to the...

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When interest is compounded continuously, the amount of money increases at a rate proportional to the amount S present at time t, that is, dS/dt = rS, where r is the annual rate of %3D interest. (a) Find the amount of money accrued at the end of 8 years when $8000 is deposited in a savings account drawing 5 % annual interest compounded continuously. (Round your answer 4 to the nearest cent.) $ (b) In how many years will the initial sum deposited have doubled? (Round your answer to the nearest year.) years 8(4) that is accrued when interest is compounded quarterly. (Round your (c) Use a calculator to compare the amount obtained in part (a) with the amount S = 8000 1 + (0.0575) 4 answer to the nearest cent.) S = $ When interest is compounded continuously, the amount of money increases at a rate proportional to the amount S present at time t, that is, dS/dt = rS, where r is the annual rate of %3D interest. (a) Find the amount of money accrued at the end of 8 years when $8000 is deposited in a savings account drawing 5 % annual interest compounded continuously. (Round your answer 4 to the nearest cent.) $ (b) In how many years will the initial sum deposited have doubled? (Round your answer to the nearest year.) years 8(4) that is accrued when interest is compounded quarterly. (Round your (c) Use a calculator to compare the amount obtained in part (a) with the amount S = 8000 1 + (0.0575) 4 answer to the nearest cent.) S = $