John is 28 years old and plans to retire at 67. He wants to have a fund at 67 th

Question

John is 28 years old and plans to retire at 67. He wants to have a fund at 67 that will let him perpetually spend $4,500 a month after retirement. Assume a continuous money flow. Answer the following. Round your answers (at the last step) to Integers. (a) Suppose that after his retirement John puts the money In a fund paying Interest at an annual rate of 4.2%, compounded continuously. Then John will need $ for his retirement. (b) Suppose that John starts to invest a fixed amount each month from now until he retires, in a fund that pays interest at an annual rate of 6.2%, compounded continuously. Then he should invest $ each month.

Explanation / Answer

a. John will need $1,259,037 for his retirement.

b. He should invest $608 each month

a. Monthly receipts required =PMT 4500 perpetual Rate 4.2% compounded continuously Hence, annual Effective rate=e^i -1 4.29% Monthly effective rate= Annual effective rate/12 0.3574% The formula for finding Present value of perpetual annuity is PMT/r Hence Amount of money in the fund on retirement should be= 4500/0.3574% 1259036.583 b Future value of money required at the age of 67 1259037 Period of investment=(67-28)*12 months 468 Rate of interest compounded continuosly 6.20% Effective rate - annual = e^I -1 6.40% Monthly rate=Effective rate/ 12 0.5330% Monthly investment is computed using the formula
=PMT(0.533%,468,,-1259037) $608.20

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