Question

2. An investment of $200 is now valued at $315. Assuming continuous compounding has

Answer 1

Answer:

An yearly interest rate of 7.57% is needed to be for this to be possible.

Step-by-step explanation:

The amount of money after t years of continuous compounding is given by:

$P(t) = P(0)e^{rt}$

In which P(0) is the initial investment and r is the interest rate, as a decimal.

In this problem, we have that:

$P(0) = 200, P(6) = 315$

We have to find r.

$P(t) = P(0)e^{rt}$

$315 = 200e^{6r}$

$e^{6r} = \frac{315}{200}$

$\ln{e^{6r}} = \ln{\frac{315}{200}}$

$6r = \ln{\frac{315}{200}}$

$r = \frac{\ln{\frac{315}{200}}}{6}$

$r = 0.0757$

An yearly interest rate of 7.57% is needed to be for this to be possible.