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

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 million dollars per year and second, you are earning 5% interest.

b. 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.

c. 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?

Expert Solution

So when t=13 or at the end of 13th year the net amount of money calculated in 1st way will overtake that in 2nd way.

Colby Messinger answered 7 months ago

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