Question

A bank pays interest continuously at the rate of 6%. How long does it take for a deposit of Q0 to grow in value to 2Q0

Answer 1

Continuously Compound Interest:

$$Q(t)=Q_0e^{rt}$$

Then

$$e^{rt}=\dfrac{Q}{Q_0}$$

$$t=\dfrac{\ln(Q/Q_0)}{r}$$

Given

$$r=0.06, Q=2Q_0$$

$$t=\dfrac{\ln(2Q_0/Q_0)}{0.06}\approx11.55(years)$$