Question

The formula A = Pe^rt calculates the amount an investment earning a nominal rate of r compounded continuously is worth. Show that the amount of time it takes for the investment to double in value is given by the expression ln2/r.

Answer 1

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