## More on the price of a can of coke (or a CD)

In response to the last comment, Flexo writes:

Thanks for the comment Flex. I'm not entirely sure I understand it though. I'll try to better explain how I worked it all out, using the CD as my example. Please (anyone) let me know if you can spot the error in my thinking. Thanks.

Okay, so if a CD costs $25 today, it will cost $25*1.03^30 = $60.68 in 30 years due to inflation (at 3%).

That same $25 if invested at 10% instead of spent would grow to be $25*1.1^30 = $436.24 in 30 years.

I guess this $436.24 is what we would call the lost opportunity cost . It is $436.24

Now what we can then do is work out what the

It perhaps isn't terribly meaningful from a financial point of view to do this conversion as there is no way we could use this $179.73 today. My main thought was that the conversion gives us a good way to understand the lost opportunity cost, given that we are used to thinking about the cost of things today, instead of in thirty years time.

My calculations do in fact take compound interest into account. Up until now it has in fact all been calculated with exponents. The multiplication factor of 7.19 is actually given by (1.1/1.03)^30. The multiplication just gives us a short-hand method for carrying out the above calculation.

(nb. this is slightly different to the answer in the original post due to differences in rounding)

I think (though I may be wrong) that what Flexo was expecting to see as a result of my calculation was the lost opportunity cost

Thanks again for the thoughtful comment Flexo.

Using the $7.18 as a factor for each current $1 won't work since interest is compounded. You're dealaing with exponents, not multiplication. The cost of a CD now will cost you much more in lost opportunity cost than $20 * 7.18.

Thanks for the comment Flex. I'm not entirely sure I understand it though. I'll try to better explain how I worked it all out, using the CD as my example. Please (anyone) let me know if you can spot the error in my thinking. Thanks.

Okay, so if a CD costs $25 today, it will cost $25*1.03^30 = $60.68 in 30 years due to inflation (at 3%).

That same $25 if invested at 10% instead of spent would grow to be $25*1.1^30 = $436.24 in 30 years.

I guess this $436.24 is what we would call the lost opportunity cost . It is $436.24

*in thirty years time*.Now what we can then do is work out what the

*equivalent*of this lost opportunity cost is today, by undoing the effects of inflation. This gives us: $436.24 / 1.03^30 = $179.73.It perhaps isn't terribly meaningful from a financial point of view to do this conversion as there is no way we could use this $179.73 today. My main thought was that the conversion gives us a good way to understand the lost opportunity cost, given that we are used to thinking about the cost of things today, instead of in thirty years time.

My calculations do in fact take compound interest into account. Up until now it has in fact all been calculated with exponents. The multiplication factor of 7.19 is actually given by (1.1/1.03)^30. The multiplication just gives us a short-hand method for carrying out the above calculation.

(nb. this is slightly different to the answer in the original post due to differences in rounding)

I think (though I may be wrong) that what Flexo was expecting to see as a result of my calculation was the lost opportunity cost

*in thirty years time*while I was actually calculating the lost opportunity cost's equivalent today (equivalent in terms of buying power, that is).Thanks again for the thoughtful comment Flexo.