Your grandfather placed $2,000 in a trust fund for you. In 10 years
the fund will be worth $5,000. What is the rate of return on the trust
fund? What if granny puts $25,000 into a bank account earning 6%. You
can't withdraw the money until the balance is $100,000.How long will
you have to leave the money in the account?

Hi pheifer!
These are two separate questions:

1) Your grandfather placed $2,000 in a trust fund for you. In 10 years
the fund will be worth $5,000. What is the rate of return on the trust
fund?

Assuming that the interest rate will be compounded annualy, the
equation we must solve here is the following:

2000*(1+r)^10 = 5000

and we must solve for r. The equation is so because if we have 2000
today, they become 2000*(1+r) in one year;
2000*(1+r)*(1+r)=2000*(1+r)^2 in two years, etc. So in ten years, 2000
become 2000*(1+r)^10. Solving this simple equation gives:

(1+r)^10 = 5000/2000 = 2.5
 1+r = (2.5)^(1/10)
 1+r = 1.0960
   r = 0.0960

Thus the rate of return is 9.6% per year.


2) What if granny puts $25,000 into a bank account earning 6%. You
can't withdraw the money until the balance is $100,000.How long will
you have to leave the money in the account?

The same formula can be used here, with another unknown. The equation
to be solved becomes:

25000*(1.06)^t = 100000

So, solving for t:

1.06^t = 100000/25000 = 4
log(1.06^t) = log(4)
t*log(1.06) = log(4)
          t = log(4)/log(1.06)
          t = 23.79

(here log refers to natural logarithm). The answer is then that you
will have to leave the money in the account for about 24 years.


I hope this was clear enough. If you have any doubt, please request a
clarification before rating the answer.

Best wishes!
elmarto