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A bank offers 7% compunded continously. How soon will a deposit: triple and how soon...
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- A is the initial amount
- P is the principal
- r is the interest rate
- t is the time in years
(Level 1) Associate Educator, Expert
The formula involved for continuous compound is as follows:
`A = Pe^(rt)`
We know that the interset rate is 7%:
`A = Pe^(0.07t)`
We want to know how long it takes for the amount to triple. Tripling the principal means that `A = 3P` . We substitute this to the equation and solve for `t` .
`A = 3P = Pe^(0.07t)`
`3P = Pe^(0.07t)`
`3 = e^(0.07t)`
`ln(3) = ln(e^(0.07t))`
`ln(3) = 0.07t`
`t = (ln(3))/(0.07)`
`t = 15.69`
Hence, the amount will triple in 15.69 years.
We want to know how long it takes before the amount increases by 25%. This means that `A = (1.25)P` . Solving this uses the same technique as the first one:
`A = 1.25P = Pe^(0.07t)`
`1.25P = Pe^(0.07t)`
`1.25 = e^(0.07t)`
`ln(1.25) = ln(e^(0.07t))`
`ln(1.25) = 0.07t`
`t = (ln(1.25))/(0.07)`
`t = 3.19`
Hence, it takes 3.19 years for the amount to increase by 25%.
Posted by mvcdc on July 8, 2013 at 2:35 PM (Answer #1)
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