Question

How long would it take to triple an investment at 4% compounded quarterly

Answer 1

$A=P(1+\frac{r}{100})^n$

$3P=P(1+\frac{4}{400})^{4n}$

Dividing by P we obtain,

$3=(1.01)^{4n}$

Taking the logarithm of both sides

$log3=4nlog1.01$

This implies that

$4n=\frac{log3}{log1.01}$

$n=\frac{log3}{4log1.01}$

$n=27. 60years$