Question 2 - PV of an Annuity Due [2 points]: Your subscription to Jogger\'s Wor

Question

Question 2 - PV of an Annuity Due [2 points]: Your subscription to Jogger's World Monthly is about to run out and you have the choice of renewing it by sending in the $10 a year regular rate or of getting a lifetime subscription to the magazine by paying $100. Your opportunity cost is 7 percent. How many years would you have to live to make the lifetime subscription the better buy? Payments for the regular subscription are made at the beginning of each year. (Round up if necessary to obtain a whole number of years.).

Explanation / Answer

Let the number of years be X.

Present value of payment of $10 each year = 10 * (1-1/(1+7%)^X) / 7% * (1+7%)

This is equal to the lifetime membership fee of 100.

So 10 * (1-1/(1+7%)^X) / 7% *(1+7%) = 100

So 1-1/(1.07)^X = 0.654

1/(1.07)^X = 0.346

(1.07)^X = 2.891

Solving, we get X = 15.69 years, rounding up to 16 years

Answer: 16 years

Hope this helped ! Let me know in case of any queries.

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