Question

5-19. Suppose your parents have just retired and have $1 million in a retirement account. For how many years can they withdraw $5,000 at the beginning of each month for expenses, assuming that the account will continue to earn a 5 percent annual return until it is exhausted?

See Problem 5-19. Now, suppose your parents have decided that they will depend on their retirement savings for 20 years. Everything else remains the same. How much money can they afford to withdraw at the beginning each month?

Answer 1

Present Value of Annuity =

where r is the rate of Return for compounding period = 0.05 / 12 = 0.00416666666

n is the no of compounding period = x

1,000,000 =

1,000,000 = 1,200,000 * 1- (1/ (1.00416666666)^n)

1- (1/ (1.00416666666)^n) = 1000,000 / 1,200,000

1- (1/ (1.00416666666)^n) = 0.83333333333

1/ (1.00416666666)^n = 1 - 0.83333333333

1/ (1.00416666666)^n = 0.1666666667

1 = 0.1666666667 * (1.00416666666)^n

(1.00416666666)^n = 1 / 0.1666666667

(1.00416666666)^n = 6

Logging both sides

n * Log 1.00416666666 = log 6

n * 0.00180580086 = 0.77815125038

n = 0.77815125038 / 0.00180580086

n = 430.92

No of years = 430.92 / 12 = 35.91 years

Present Value of Annuity =

where r is the rate of Return for compounding period = 0.05 / 12 = 0.00416666666

n is the no of compounding period = 20 years * 12 = 240

1000,000 =  

1,000,000 = Periodic Cash Flow * 151.525313176

Periodic Cash Flow = 1,000,000 / 151.525313176

Periodic Cash Flow = 6599.56

6600 can be withdrawn every months.