# Thread: Compouind interest

1. ## Compouind interest

You being the wise parent invest $25000 for your newborn child's college education. Setting your sights high, you arrive at a figure of$150,000 needed for the education expenses. If you can get a 9% annual rate, compounded monthly, how old will your child be when you will have the funds to send her to college?

2. Originally Posted by tony351
You being the wise parent invest $25000 for your newborn child's college education. Setting your sights high, you arrive at a figure of$150,000 needed for the education expenses. If you can get a 9% annual rate, compounded monthly, how old will your child be when you will have the funds to send her to college?
Since it's monthly compounding, we need to adjust our interest rate. 9% per year is .75% per month

We have:

$25000 * (1.0075)^n = 150000$

$(1.0075)^n = 6$

Take the natural log of both sides:

$n * Ln(1.0075) = Ln(6)$

$n = 239.796$ months $\approx$ 19.983 years

Depending on how your answer needs to be, that's exact time. If you need exact years or months, you can do that to.

To check that, see what happens when you roll up 25,000 for 239.796 months @ .75%/month. That's your check and balance system.

3. ## Can you explain further

Did the 1.09 come from adding 1 to the 9% and where did the 6 come from? Dumb question, I know

4. Originally Posted by tony351
Did the 1.09 come from adding 1 to the 9% and where did the 6 come from? Dumb question, I know
I just saw that you had monthly as the basis for interest. I corrected my post above. The 6 = 150000/25000.

With the correction, 1.0075 = 1 + (.09/12)

You add 1 because a balance is principal + interest. So P(1 + i) = P + Pi where Pi is the interest on the balance.