Question

Your subscription to Investing Wisely Weekly is about to expire. You plan to subscribe to the magazine for the rest of your life, and you can renew it by paying $85 annually, beginning immediately, or you can get a lifetime subscription for $850, also payable immediately. Assuming that you can earn 6.0% on your funds and that the annual renewal rate will remain constant, how many years must you live to make the lifetime subscription the better buy?

	a.	14.76
	b.	14.33
	c.	14.18
	d.	15.47
	e.	17.77

Answer 1

PV of Annuity Due = Annual Payment + Annual Payment * [{1 - (1 + r)^-(n-1)} / r]

$850 = $85 + $85 * [{1 - (1 + 0.06)^-(n-1)} / 0.06]

$850 - $85 = $85 * [{1 - (1.06)^-(n-1)} / 0.06]

$765 / $85 = [{1 - (1.06)^-(n-1)} / 0.06]

9 * 0.06 = 1 - (1.06)^-(n-1)

(1.06)^-(n-1) = 1 - 0.54

-(n-1)[log(1.06)] = [log(0.46)]

-(n-1)[0.0583] = -0.7765

n-1 = -0.7765 / -0.0583

n = 13.33 + 1 = 14.33 years

Option "b" is correct.