Question

Suppose you have $800,000 in your savings account when you retire. Your plan is to withdraw $6,000 a month as retirement income from this account. You expect to earn annual interest of 6 percent, compounded monthly, on your money during your retirement. How many months can you be retired until you run out of money?

	a.	285.14
	b.	210.83
	c.	262.59
	d.	220.27

The dividends paid by a corporation

	a.	are tax-deductible, i.e., reduce the taxable income of the corporation
	b.	to an individual become non-taxable income to that individual
	c.	to another corporation receive preferential tax treatment (70% tax exclusion)
	d.	to an individual become taxable income of that individual and receive 30% tax exclusion

Which one of the following bonds has the greatest interest rate (price) risk?

	a.	10-year; 9 percent coupon
	b.	10-year; 4 percent coupon
	c.	15-year; 9 percent coupon
	d.	15-year; 4 percent coupon

Answer 1

Given,

Present value = $800000

Annual withdrawal (A) = $6000

Annual interest rate = 6% or 0.06

Solution :-

Monthly interest rate (r) = 0.06/12 = 0.005

Let number of months be 'n'

Now,

Present value = A/r x [1 - (1 + r)^-n]

$800000 = $6000/0.005 x [1 - (1 + 0.005)^-n]

$800000 x 0.005/$6000 = 1 - (1.005)^-n

0.6666666667 = 1 - (1.005)^-n

(1.005)^-n = 1 - 0.6666666667

(1.005)^-n = 0.3333333333

Taking 'Log' both sides,

Log(1.005)^-n = Log(0.3333333333)

-n.Log(1.005) = Log(0.3333333333)

-n.(0.0049875415) = -1.0986122888

n = -1.0986122888/-0.0049875415

n = 220.27

So, number of months = 220.27 months

Option 'd' is correct.