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 interest. (a) Find the amount of money accrued at the end of 3 years when $6000 is deposited in a savings account drawing 5% annual interest compounded continuously. (Round your answer to the nearest cent.) $ (b) In how many years will the initial sum deposited have doubled? (Round your answer to the nearest year.) years (c) Use a calculator to compare the amount obtained in part (a) with the amount S= 6000 = 6000(1 + (0.0575)) **) that is accrued when interest is compounded quarterly. (Round your 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 interest. (a) Find the amount of money accrued at the end of 3 years when $6000 is deposited in a savings account drawing 5% annual interest compounded continuously. (Round your answer to the nearest cent.) $ (b) In how many years will the initial sum deposited have doubled? (Round your answer to the nearest year.) years (c) Use a calculator to compare the amount obtained in part (a) with the amount S= 6000 = 6000(1 + (0.0575)) **) that is accrued when interest is compounded quarterly. (Round your answer to the nearest cent.) S = $
Algebra and Trigonometry (MindTap Course List)
4th Edition
ISBN:9781305071742
Author:James Stewart, Lothar Redlin, Saleem Watson
Publisher:James Stewart, Lothar Redlin, Saleem Watson
Chapter4: Exponential And Logarithmic Functions
Section4.CT: Chapter Test
Problem 11CT
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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 interest.
3
(a) Find the amount of money accrued at the end of 3 years when $6000 is deposited in a savings account drawing 5 % annual interest compounded continuously. (Round your answer to the nearest cent.)
$
(b) In how many years will the initial sum deposited have doubled? (Round your answer to the nearest year.)
years.
(c) Use a calculator to compare the amount obtained in part (a) with the amount S 6000
6000 (1 + 1 (0.0575)³(4) that is accrued when interest is compounded quarterly. (Round your answer to the nearest cent.)
S = $](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F3b921adb-efc9-4226-8cca-3236f11f14ed%2Fb505b5cb-fa0f-4bb9-b64e-e944555a56e4%2Fggc23nq_processed.png&w=3840&q=75)
Transcribed Image Text: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 interest.
3
(a) Find the amount of money accrued at the end of 3 years when $6000 is deposited in a savings account drawing 5 % annual interest compounded continuously. (Round your answer to the nearest cent.)
$
(b) In how many years will the initial sum deposited have doubled? (Round your answer to the nearest year.)
years.
(c) Use a calculator to compare the amount obtained in part (a) with the amount S 6000
6000 (1 + 1 (0.0575)³(4) that is accrued when interest is compounded quarterly. (Round your answer to the nearest cent.)
S = $
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