1 pt A bank account earns 3 annual interest compounded conti

(1 pt) A bank account earns 3% annual interest compounded continuously. You deposit $48,000 in the account and withdraw money continuously from the account at a rate of $900 per year. (a) Write a differential equation describing the balance B in the account after t years. B\'= (b) What is the equilibrium solution to the differential equation? (f his is the amount that must be deposited now for the balance to stay the same over the years. Answer: (c) Find the solution to the differential equation. Answer: (d) How much is in the account after 20 years? Answer:

Solution

Principal = 48000

Annual additions = interest at 3%

Withdrawals =900 per year

Increase is at the rate of 0.03t and decrease 900

Hence after 1 years interest earned with amount= 48000(1.03)

Interest = 48000(0.03)

Withdrawal =900

Net increase in 1 year = 1440-900 =540

II year net increase = (48000-900)0.03-900

III year = (48000-900-900)0.03 -900-900

Hence after n years rate of increase B\' = (48000-900n)0.03-900 (n-1)

or B\' = 2340--927n

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If B\' =B

then B\' = (B-900n)0.03-900(n-1)