Question

Try a similar problem using the formula for continuously compoundinginterest.If $10,000 is invested in a savings account that pays 8.65% interestcompounded continuously, how many years will it take for the balance togrow to $250,000?Substitute the variable values into the formula.250,000 = 10,000 20.0865tTo isolate the base e expression, divide by 10,000.25 = 0.08650Now the equation should look familiar. Instead of asking how long it will takefor the money to double, you are asking how long it will take to grow 25 timesgreater in value.

Answer 1

we have the expression

`25=e^((0.0865t))`

solve for t

Apply ln both sides

`\begin{gathered} \ln (25)=\ln (e^((0.0865t))) \\ \ln (25)=0.0865t\cdot\ln (e) \\ \ln (25)=0.0865t \\ \end{gathered}`

t=37.2 years