The formula A = Pe^rt calculates the amount an investment earning a nominal rate of r compounded continuously is worth. Show tha
t the amount of time it takes for the investment to double in value is given by the expression ln2/r.
1 answer:
Answer:
t = In2/ r
Step-by-step explanation:
Given the formula : A = Pe^rt
For investment to double ;
Final amount (A) = 2 * initial investment (p)
A = 2p
Hence,
2p = pe^rt
2 = e^rt
Take the In of both sides
In2 = rt
Divide both sides by r
In2 /r = rt /r
In2/ r = t
t = In2/ r ; Hence, the proof
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