Question

3. Congratulations, you just won the lottery! In one option presented to you, you will be paid one

million dollars a year for the next 25 years. You can deposit this money in an account that will earn

5% each year.

(a) Let M(t) be the amount of money in the account (measured in millions of dollars) at time

t (measured in years). Set up a differential equation that describes the rate of change in the

amount of money in the account. Two factors cause the amount to grow – first, you are

depositing one millon dollars per year and second, you are earning 5% interest.

(b) If there is no amount of money in the account when you open it, how much money will you

have in the account after 25 years?

(c) The second option presented to you is to take a lump sum of 10 million dollars, which you

will deposit into a similar account. Set up a new initial value problem (that is, differential

equation with initial condition) to model this situation.

(d) How much money will you have in the account after 25 years with in this case?

(e) Do you prefer the first or second option? Explain your thinking.

(f) At what time does the amount of money in the account under the first option overtake the

amount of money in the account under the second option?

Answer 1