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How long would it take to double your principal in an account that pays 6.5% annual interest compounded continuously? round your answer to one decimal place?

User Maria Minh
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2 Answers

3 votes

Answer:

11 years

Explanation:

User Mehmet Guloglu
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5 votes
It would take 10.7 years.

The formula for continuously compounded interest is:

A=Pe^(rt)
where P is the principal, r is the interest rate as a decimal number, and t is the number of years.

Using our information we have:

A=Pe^(0.065t)

We want to know when it will double the principal; therefore we substitute 2P for A and solve for t:

2P=Pe^(0.065t)

Divide both sides by P:

(2P)/(P)=(Pe^(0.065t))/(P) \\ \\2=e^(0.065t)

Take the natural log, ln, of each side to "undo" e:

ln(2)=\ln{e^(0.065t)} \\ \\0.6931471806=0.065t

Divide both sides by 0.065:

(0.6931471806)/(0.065)=(0.065t)/(0.065) \\ \\10.7\approx t
User Kashawn
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