SOLUTION: how long it takes a $1200 investment to earn $200 interest if it is invested at 9% interest compounded quarterly?

Question 543333: how long it takes a $1200 investment to earn $200 interest if it is invested at 9% interest compounded quarterly?
Answer by jpg7n16(66) (Show Source): You can put this solution on YOUR website!
You're looking for the compounding formula:

where
"A" = amount you will ultimately have in the account (A=1200+200=1400)
"P" = amount you started with, aka principal (p=1200)
"i" = interest rate per year (i=9%)
"m" = number of compounding periods per year (Quarterly means m=4)
"n" = number of years (n=??? - this is what you're solving for)
Plug into the formula and solve for N.
.

.
Here's where most people give up. They don't remember how to bring the variable in the exponent down to work with. The solution -> natural log function!

Example: Take

and
So
It allows you to bring the exponent down so it's workable.
.
So what we need to do now is apply the ln function to both sides of the equation. And remember ln(some number) is a constant. You can calculate it or divide by it.
.

Time to bust out the calculator

So it takes approx 1.732 years (20.78 months) to earn $200 of interest.
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