If $500 is invested at 7% compounded continuously, how long would it take for the value of the investment to reach $800?
The equation for continuous compounding is
where
P = the Principal, which is the same as the starting amount = $500
A = the AFTER amount, which is the same as the ending amount = $800
r = the rate expressed as a decimal, 0.07
t = the number of years it takes for the Principal to become the
AFTER amount. That's the unknown that we want to find.
e = 2.718281828459
So we substitute everything but t in
Divide both sides by 500
Use this rule:
The exponential equation is equivalent to
Divide both sides by .07:
About 6.7 years.
Edwin