When interest is compounded continuously, the amount of money increases at a rat

Question

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. Find the amount of money accrued at the end of 6 years when $8000 is deposited in a savings account drawing 5-3/4% 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 Use a calculator to compare the amount obtained in part (a) with the amount S = 8000(1 + 1/4(0.0575))^6(4) that is accrued when interest is compounded quarterly. (Round your answer to the nearest cent.) S = $

Explanation / Answer

Solution:

  (a) A = 8000e(0.0575*6) = $11295.92

(b) 16000 = 8000e(0.0575t) ===> 2 = e(0.0575t) ===> ln(2) =0.0575t  

t = ln(2) /0.0575 = 12.05473357 years

(c) A = 8000(1 + 0.0575/4)(4*6) = $11248

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