(Solution Library) When interest is compounded continuously, the amount of money increases at a rate proportional to the amount S present at time t, that is, d S
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, \(d S / d t=r S\), where \(r\) is the annual rate of interest.
- Find the amount of money accrued at the end of 5 years when $5000 is deposited in a savings account drawing \(5 \frac{3}{4} \%\) annual interest compounded continuously.
- In how many years will the initial sum deposited have doubled?
- Use a calculator to compare the amount obtained in part (a) with the amount \(S=5000\left(1+\frac{1}{4}(0.0575)\right)^{5(4)}\) that is accrued when interest is compounded quarterly.
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(See Steps) The indicated function y_1(x) is a solution of the
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