Your subscription to BusinessWeek is about to expire. You plan to subscribe to the magazine for the rest of your life. You can renew it by paying $50 annually, beginning immediately, or you can get a lifetime subscription for $500, also payable immediately. Assuming that you can earn 6.525% 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) 12
B) 15
C) 10
D) 18

Question

Quizplus · Accepted Answer

To find out the number of years required to make the lifetime subscription the better buy, we need to compare the present value of the annual subscription with the present value of the lifetime subscription.

Let’s calculate the present value of renewing annually using the perpetuity formula:

PV = C/i, where C is the annual payment and i is the discount rate.

PV = $50/0.06525 = $766.79

Now, let’s calculate the present value of the lifetime subscription:

PV = $500

To find out how many years we need to live for the lifetime subscription to be more beneficial, we need to find the future value of $500 over the number of years we live, and compare it to the total cost of renewing annually over the same period.

FV = PV(1+i)^n, where FV is the future value, n is the number of years we live.

So, let’s solve for n:

$500(1+0.06525)^n = $766.79[(1+0.06525)^n - 1]/0.06525

(1.06525)^n = ($766.79 x 0.06525 + $500)/$500

(1.06525)^n = 1.24758

n = ln(1.24758)/ln(1.06525)

n ≈ 14.97

Therefore, we need to live for approximately 15 years for the lifetime subscription to be the better buy. The correct answer is B.

Your Subscription to BusinessWeek Is About to Expire