Question

# When interest is compounded continuously, the amount of money increases at a rate proportional to the...

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 \$5000 is deposited in a savings account drawing 5 3/4

% annual interest compounded continuously. (Round your answer to the nearest cent.)

\$

(b) this is the part I’m having the hard time with.

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 = 5000

1 +

 1 4

(0.0575)

 8(4)

that is accrued when interest is compounded quarterly. (Round your answer to the nearest cent.)

S = \$

for any doubt feel free to ask.

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