Question

On your 21st birthday, your uncle told you that in the current volatile economic climate you should read Capitalizing Astutely, a monthly journal. He tells you to choose. He would pay for the subscription annually, $89.99, beginning immediately or pay for a lifetime subscription of $950. Assuming that he can earn 5% on his funds and that the annual renewal rate will remain constant, how old will you be when the lifetime subscription is a better buy?
(Hint: if you are using Excel, do not forget for prompt type, input “1”)

Answer 1

Answer = 35 years old.

Explanation and calculation:

Cost of annual subscription = $89.99

Let the no. of years be "x" which will make the present value of annual subscription = value of lifetime subscription.

Thus: 89.99 + 89.99/1.05^1 + 89.99/1.05^2.....89.99/1.05^x = 950

In other words lifetime subscription will be a better buy when 89.99 + 89.99/1.05^1 + 89.99/1.05^2.....89.99/1.05^x > 950

Using excel we can see that 13 years from now the present value of annual payments of $89.99 for 13 years = $935.32

Thus PV(5%, 14, 89.99, 1) = $935.32

In the above PV function the total no. of payments period = 14 because the payment starts immediately. Hence 13+1 = 14

Thus till you are 21+13 = 34 years old annual subscription will be better.

The lifetime subscription becomes better when you are 34+1 = 35 years old

This is because when you are 35 years old a total of 15 payments have been made. Thus PV(5%, 15, 89.99, 1) = 980.77 and this exceeds the amount of $950.