Question

Ron deposits $2,000 into an account that receives 3.1% interest compounded continuously. How much money is in the account after 9 years?

Answer 1

In general, the continuous compounding interest formula is

$\begin{gathered} P(t)=Pe^{rt} \\ P\rightarrow\text{ initial amount} \\ t\rightarrow\text{ time} \\ r\rightarrow\text{ interest rate} \end{gathered}$

Therefore, in our case,

$P(t)=2000e^{0.031t}$

Set t=9 as shown below

$\Rightarrow P(9)=2000e^{0.279}\approx2643.615...$

The exact answer is 2000e^(0.279)