Question

How many years will it take an initial investment of $25,000 to triple to $75,000 at an annual rate of 7% compounded continuously

Answer 1

`t = 15.7`

Explanation:

Given

`Principal = 25000` --- P

`Amount = 75000` --- A

`Rate = 7\%` --- R

Required

Determine the time (t)

Using continuous growth formula:

We have

`A = Pe^(rt)`

Convert rate to decimal

`Rate = 7\%`

`r = 0.07`

Substitute values for A, P and r

`75000 = 25000 * e^(0.07t)`

Divide both sides by 25000

`3 = e^(0.07t)`

Rewrite the exponential function as logarithmic, we have:

`ln3 = 0.07t`

Reorder

`0.07t = ln3`

Divide both sides by 0.07

`t = (ln3)/(0.07)`

`t = (1.09861228867)/(0.07)`

`t = 15.69`

`t = 15.7`

Hence, the time is approximately 15.7 years