Question 1104177
How long (in years) would $600 have to be invested at 11.2%, compounded continuously, to earn $400 interest?
 (Round your answer to the nearest whole number.) 
:
The continuous interest formula: {{{A = P*e^(rt)}}}, where:
A = amt after t time
P = initial amt
r = interest rate in decimal form
t = time in years
When we have $400 interest, the accumulated amt: 600+400 = 1000
{{{1000 = 600*e^(.112t)}}}
we can rewrite it to
{{{600*e^(.112t)=1000}}}
{{{e^(.112t)=1000/600}}}
reduces to
{{{e^(.112t)=5/3}}}
using natural logs, ln of e is 1 therefore
{{{.112t = ln(5/3)}}}
.112t = .5108256
t = {{{.5108256/.112}}}
t = 4.56 ~ 5 years to earn $400 interest