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 $75 annually,beginning immediately,or you can get a lifetime subscription for $750,also payable immediately.Assuming you can earn 5.5% on your funds and the annual renewal rate will remain constant,how many years must you live to make the lifetime subscription the better buy? Round fractional years up.(Hint: Be sure to remember that you are solving for how many years you must live,not for how many payments must be made.)
A)10
B)11
C)12
D)13

Question

Quizplus · Accepted Answer

To determine the better buy between the annual subscription and the lifetime subscription, we compare the present value of paying $75 annually indefinitely at a 5.5% interest rate to the one-time payment of $750 for the lifetime subscription. The formula for the present value of a perpetuity is PV = P / r, where P is the payment ($75) and r is the interest rate (0.055). Thus, PV = $75 / 0.055 = $1363.64. Since the lifetime subscription costs $750, it becomes the better option when the present value of the annual payments exceeds $750. To find the number of years until the lifetime subscription is the better option, we compare the present value of paying $75 annually for n years to $750. This involves calculating the present value of an annuity, but since the question asks for a direct comparison and rounding up fractional years, we estimate based on the given options. The correct answer is found by calculating or estimating when the cost of annual payments, discounted back at 5.5%, equals or exceeds $750. The calculation involves more detailed financial math, but the hint suggests we're looking for the point at which the lifetime subscription saves money compared to the ongoing annual payments. Given the options and the nature of the calculation, rounding up fractional years leads to the conclusion that after 13 years, the lifetime subscription becomes the better financial decision.

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