For instance, suppose that one opens an individual retirement account (IRA) at age 25 and makes annual investments of $\$ 2000$ thereafter in a continuous manner. Assuming a rate of return of $8 \%$, what will be the balance in the IRA at age 65 ?
We have $S_0=0, r=0.08$, and $k=\$ 2000$, and we wish to determine $S(40)$. From Eq. (16) we have
$$
S(40)=(25,000)\left(e^{3.2}-1\right)=\$ 588,313
$$
