Differential Equations (Applications)

When Mr. Teng retired on 1 January 2018, he put a sum of 10,000 into a senior citizen fund that has a constant rate of return of 5% at the end of every month. Starting in February 2018, he withdraws500 at the start of each month for groceries. Denote the amount of money that Mr. Teng has at the time n years by $x.

(i) The differential equation relating x and n can be written in the form of \frac{dx}{dn}= kx+c. State the values of k and c.

(ii) Solve the differential equation and find the amount of money that Mr. Teng has after 15 months.

(iii) In which month will Mr. Teng no longer be able to withdraw the full $400?

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