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 7 years when $9000 is deposited in a savings account drawing 5% annual interest compounded continuously. (Round your answer to the nearest cent. $ 11702 (b) In how many years will the initial sum deposited have doubled? (Round your answer to the nearest year.) 12 years (c) Use a calculator to compare the amount obtained in part (a) with the amount S = 900 7(4) that is accrued when interest is compounded quarterly. (Round your answer to the nearest 1+ cent.) S= $

Principles of Accounting Volume 2
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ISBN:9781947172609
Author:OpenStax
Publisher:OpenStax
Chapter11: Capital Budgeting Decisions
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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 7 years when $9000 is deposited in a savings account drawing 5% annual interest compounded continuously. (Round your answer to the nearest cent.
$ 11702
(b) In how many years will the initial sum deposited have doubled? (Round your answer to the nearest year.)
12
years
(c) Use a calculator to compare the amount obtained in part (a) with the amount S = 900
7(4)
that is accrued when interest is compounded quarterly. (Round your answer to the nearest
1+
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 7 years when $9000 is deposited in a savings account drawing 5% annual interest compounded continuously. (Round your answer to the nearest cent. $ 11702 (b) In how many years will the initial sum deposited have doubled? (Round your answer to the nearest year.) 12 years (c) Use a calculator to compare the amount obtained in part (a) with the amount S = 900 7(4) that is accrued when interest is compounded quarterly. (Round your answer to the nearest 1+ cent.) S= $
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