Jenna has just entered collage and has decided to quit smoking. She wants to regain her health and save money in the process. She smokes two packs a day, which translates into roughly $30 per week.
Suppose she makes weekly deposits of this money into a bank account that pays annual interest of 10%, compounded continuously.
What will be balance of Jenna's account when she retires in 47 years?
(Hint: If an initial amount of so dollars is deposited in a bank that pays an annual interest of r, compounded continuously, then the future value, S(t), of the account satisfy the initial-value problem d/dt=rs, S(O)=So.
Moreover, if deposits amounting to d dollars per year (made uniformly throughout the year) are made into the above account, then the future value of this new account, called an annuity, will satisfy ds/dt=rS+d, S(0)=So.