Question

A sum of money is invested at 12% compounded quarterly. About how long will it take for the amount of money to double?

Answer 1

Answer:

  5.9 years

Step-by-step explanation:

We believe a better representation of the compound interest formula is ...

  $V(t)=P(1+\dfrac{r}{n})^{nt}$

We want to find the value of t for P=1 and V(t)=2. We are told n=4, so the formula becomes ...

  $2=(1+\dfrac{.12}{4})^{4t}\\\\\log{(2)}=4t\log{(1.03)}\quad\text{take logs}\\\\t=\dfrac{\log{2}}{4\log{1.03}}\approx\boxed{5.9\quad\text{years}}$