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Question Number 60441 by ajfour last updated on 21/May/19

$$\mathrm{If}\mathrm{a}\mathrm{sum}\mathrm{of}\mathrm{money}\mathrm{doubles}\mathrm{itself}$$$$\mathrm{in}\mathrm{a}\mathrm{time}\mathrm{T},\mathrm{when}\mathrm{compounded}$$$$\mathrm{continuously},\mathrm{find}\mathrm{the}\mathrm{rate}\mathrm{of}$$$$\mathrm{interest},\mathrm{in}\mathrm{terms}\mathrm{of}\mathrm{T}.$$

Answered by tanmay last updated on 21/May/19

$$A=P{(1+\frac{R}{100})}^T$$$$A=2P$$$$2P=P{(1+\frac{R}{100})}^T$$$${\left(2\right)}^{\frac{1}{T}}=1+\frac{R}{100}$$$$R=100[2^{\frac{1}{T}}-1]$$

Commented by ajfour last updated on 21/May/19

$$\mathrm{have}\mathrm{you}\mathrm{assumed}\mathrm{annual}\mathrm{compounding},$$$$\mathrm{Sir},\mathrm{but}\mathrm{i}\mathrm{meant}\mathrm{continous}$$$$\mathrm{compounding}..$$

Commented by tanmay last updated on 21/May/19

$$yesicouldnotunderstsnd..$$

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