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Find the amount of money accrued at the end of 8 years when $3000 is deposited in a savings account drawing 5% annual interest compounded continuously. (Round your answer to the nearest cent.) $ In how many years will the initial sum deposited have doubled? (Round your answer to the nearest year.) years

Find the amount of money accrued at the end of 8 years when $3000 is deposited in a savings account drawing 5% annual interest compounded continuously. (Round your answer to the nearest cent.) $ In how many years will the initial sum deposited have doubled? (Round your answer to the nearest year.) years

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter5: Inverse, Exponential, And Logarithmic Functions
Section5.3: The Natural Exponential Function
Problem 40E
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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. (a) Find the amount of money accrued at the end of 8 years when $3000 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 = 300 = 3000(1 + (0.0525)*(*) that is accrued when interest is compounded quarterly. (Round your answer to the nearest cent.) S = $
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. (a) Find the amount of money accrued at the end of 8 years when $3000 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 = 300 = 3000(1 + (0.0525)*(*) that is accrued when interest is compounded quarterly. (Round your answer to the nearest cent.) S = $
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