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 = $
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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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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