Problem 5. (20%) A retired government employee put all his savings into a fund that has...

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Problem 5. (20%) A retired government employee put all his savings into a fund that has a 6% annualized rate of return under continuous compounding. Suppose after retirement, the retiree continuously draw his living expenses from the fund, which is 0.6 million NTD per year uniformly. Let P(t) be the value of the retiree's investment (in million NTD) left in the fund at time t (in years). We can then come up with the following differential equation: ---(0.6-P. (6%)) (a) (10%) Find the general solution for the differential equation. You may assume P(t) < 10. (b) (5%) Suppose at the time of retirement (t = 0), the retiree invests all his savings, Po million NTD, into the fund, so that P(0) - Po. Find the particular solution of the differential equation. (c) (5%) The retiree would like his pension to last for at least 20 years. Find the minimal amount of money he has to put in the fund at his retirement. (You may use the approximation e-1.2 ≈ 0.3) dP dt Problem 5. (20%) A retired government employee put all his savings into a fund that has a 6% annualized rate of return under continuous compounding. Suppose after retirement, the retiree continuously draw his living expenses from the fund, which is 0.6 million NTD per year uniformly. Let P(t) be the value of the retiree's investment (in million NTD) left in the fund at time t (in years). We can then come up with the following differential equation: ---(0.6-P. (6%)) (a) (10%) Find the general solution for the differential equation. You may assume P(t) < 10. (b) (5%) Suppose at the time of retirement (t = 0), the retiree invests all his savings, Po million NTD, into the fund, so that P(0) - Po. Find the particular solution of the differential equation. (c) (5%) The retiree would like his pension to last for at least 20 years. Find the minimal amount of money he has to put in the fund at his retirement. (You may use the approximation e-1.2 ≈ 0.3) dP dt

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a To find the general solution for the differential equation we can separate the variables and integ... View the full answer