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) 14.18
C) 14.33
D) 15.47
E) 17.77

Question

Quizplus · Accepted Answer

To determine the number of years needed 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.

For the annual subscription, the present value can be calculated using the perpetuity formula:
PV = C/r, where PV is the present value, C is the annual payment, and r is the discount rate. In this case, C = $85 and r = 6.0%. Therefore, the present value of the annual subscription is:

PV_annual = $85/0.06 = $1,416.67

For the lifetime subscription, the present value can be calculated by discounting the future payments using the present value of a lump sum formula:
PV = FV/(1+r)^n, where FV is the future value, n is the number of years, and r is the discount rate. In this case, FV = $850 and r = 6.0%. Therefore, the present value of the lifetime subscription is:

PV_lifetime = $850/(1+0.06)^0 + $850/(1+0.06)^1 + $850/(1+0.06)^2 + ... + $850/(1+0.06)^n

Solving for n using a financial calculator or spreadsheet, we get n = 14.33 years. Therefore, you need to live for at least 14.33 years to make the lifetime subscription the better buy.

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