4. 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 S. 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 ds/dt=rs, S(0)-S,. 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)=S..
4. 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 S. 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 ds/dt=rs, S(0)-S,. 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)=S..
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
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Transcribed Image Text:4. 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 S. 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 ds/dt=rs, S(0)-S,. 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)=S..
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