Question

If $8500 is invested at 12.7% compounded continuously, the future value S at any time t (in years) is given by the following formula. (Round your answers to two decimal places.) S = 8500e0.127t

(a) What is the amount after 18 months? S = $

(b) How long before the investment doubles? t = yr

Answer 1

Given formula is :

S =
`8500e^(0.127t)`

We have p = 8500

r = 12.7% or 0.127

(a) when t = 18 months or
`(18)/(12)=1.5` years

S =
`8500e^(0.127(1.5))`

=
`8500e^(0.1905)`

=
`e^(0.1905)`= 1.20985

S = $10283.73

(b) Investment doubles means S =
`8500*2=17000`

`17000=8500e^(0.127t)`

`(17000)/(8500)=e^(0.127t)`

=>
`2=e^(0.127t)`

Taking log on both sides

`ln(2)=ln(e^(0.127t))`

We get t = 5.45 years