Expert: Chanda Walker - 1/9/2009

Question
Formula A=P(1 + t/n)nt   round answer to one demical place.  amount invested $72.50, compounding periods 12, annual interest rate 6.5%  Accumulated amount $15,000, i  need to know how to set it up and the time in years

Answer
Since your formula isn't exactly right, I'll derive it for you.

A = P + I
A = P + P(rate/number of periods)

The interest for the first month is:

$72.50 * .065/12
= $0.39

A = P + I = $72.50 + $0.39 = $72.89

For the second month, we do this again

A = P + I = P + (P * r/n) + (P + (P*r/n))*r/n
         = P(1 + r/n) + P(1 + r/n)*r/n
         = P(1 + r/n)(1 + r/n)
         = P(1 + r/n)^2
         
After one year
A = P(1+r/n)^12

That can be generalized to
A = P(1 + r/n)^nt

where t is the number of years, P is the principal, r is the annual interest rate, n is the number of compounding periods in a year and A is the accumulated value.

$15000 = $72.50(1 + 0.065/12)^12t
(15000/72.50) = (1 + 0.0054)^12t
206.9 = 1.0054^12t
ln(206.9) = 12 t ln(1.0054)
5.33/(12 *.0054) = t
t = 82.25

After rounding, it take 82.4 years to accumulate $15000.