Question

How long would it take an investment of $6000 to amount to $9000 if interest is earned at 7% compounded continuously ?.

Answer 1

1. Ask yourself what you want to find ? - You want to find time ( how long it would take )

2.Clue in question - Continuous compounding

3.Use formula FV=PV.e(r.t)
Where FV=Future Value, PV=present value, e=exponent (ln) , r=rate expressed as a decimal , t=time in years

4.Plugging in the information given
9'000=6000.e(.07.t)
9'000/6000=e(.07t)
1.5=e(.07t)
Taking ln
ln(1.5)=lne (lne=1)(.07t)
using scientific cal(ln1.5).40546=1(.07t)
.40546/.07=t
5.8=t
5.8 years or 5 years 9 months and 18 days

Answer 2

correct , small point .....

after 1.5 = e^(.07t)
ln 1.5 = .07 lne
.07t = ln 1.5 , since lne = 1
t = ln 1.5/.07
= 5.79....

don't put (lne=1) as part of your solution line,