Question

How do you do this ? Todd invests 7,000 dollars at an annual interest rate of 4.2% compounded continuously. Determine how many years, to the nearest 10th of a year, it will take for Todd’s investment to triple.

Answer 1

Your answer lies with a pert... and its 26.2 years (a long time)

Explanation:

`A=Pe^(rt)` or Amount equals Principal times the mathematical constant e, to the power of the rate of interest ( r ) times the time in years ( t ).

The solution will be t , when A is three times Todd's initial investment. Do some math (3 * 7,000) and convert 4.2% into a decimal (4.2/100) and you get numbers to plug into our equation `21,000=7,000e^(.042t)`
Now solve for t

Divide both sides by 7,000
`(21,000)/(7,000)=(7,000e^(.042t))/(7,000)`

`3=e^(.042t)`

Rewrite this as a Logarithmic equation.
Now remember that a Log with the base of e can also be written as LN or the Natural Log.
So, `LN(3)=.042t`

Divide both sides by .042
`(LN(3))/(.042)=(.042t)/(.042)`

and as Per (see what I did there) the problem asks, round off to the first decimal place.

`26.2=t` Don't forget your units (years) and you're good to go :)