A magazine subscription is running out and you can renew it by sending $10 a year (the regular rate) or get a lifetime subscription to the magazine for $100. Your cost of capital is 7%. How many years would you have to live to make the lifetime subscription the better buy

15.7 years

Explanation:

We employ a mathematical approach to solve this;

Present value (PV) of $10 per year at start of year, for n years = $100 (lifetime subscription, life = n years)

Now, we need to get the equivalent amount at the end of each year. This is obtainable from the cost of capital. Which is 7% and that is same as 0.07.

Therefore, we are expecting a value of 1+0.07 = 1.07 and this brings the equivalent amount at the end of each year = 10*1.07

Now, this equivalent amount at the end of each year will give;

(10*1.07)(1.07^n - 1)/(0.07*1.07^n) = 100

Where n is the number of years

n = 15.7 years

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it should be