William W. answered • 02/22/19
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Assuming that the interest is only compounded once a year (compounded annually) then the equation for the future value (V) of sum of present money (P) is:
V = P(1+r)t
Dividing both side by P we get:
V/P = (1 + r)t
But we are looking for the time when V/P = 3 (the future value is 3 times the present value) so:
3 = (1+ r)t
We can solve this by taking the logarithm of both sides of the equation:
log(3) = log(1 + r)t
One of the rules of logarithms is that log(mn) = n*log(m) so we can apply this rule to get:
log(3) = t*log(1 + r)
Now we can divide both sides of the equation by log(1 + r) to get:
log(3)/log(1+r) = t
So the number of years to triple is (log(3)/log(1 + r)
William W.
If the interest is being compounded more than once a year we would change the basic equation to V = P(1+r/n)^tn where n is the number of compounding periods and re-solve for t02/22/19