Question

How long will it take $40,000 to grow to $110,000 if it is compounded continuously at 6%

Answer 1

The formula for continuous compounding is given by

A = P.
`e^(rt)`

where P is the initial or principal amount = $40,000

A is the amount at the end =$ 110,000

r is the rate of interest = 6% = 0.06

t is the time = the value we need to find

lets plug in the values

`110000= 40000 . e^((0.06.t))`

`(110000)/(40000) = e^(0.06t)`

`2.75= e^(0.06t)`

㏑(2.75) = ㏑[
`e^(0.06t)`]

㏑(2.75) = 0.06t

`1.0116 = 0.06t`

`t= (1.0116)/(0.06)`

t= 16.86 years

The time taken for $40000 to amount to $110000 is 16.86 years