For one insurance contract I have the option to pay 6 or 12 months in advance and get a cashback for that. For 6 months it is 2%, for 12 months it is 4%. The general assumption for this article is that the rate is cheap enough that I can afford to pay a whole year in advance, that I have 11 monthly rates available.
At first it is obvious that one should take the cashback because that is a cost saving of 4%. However, I could just invest the spare money and pay the rates with my monthly salary. Perhaps that would give a better result?
So there are two models:
I take the spare money (11 monthly rates) and put it into my portfolio. Since it is a long term investment, let's say I get 6% interest. The insurance rates are paid with the monthly salary. At the end of the insurance period I take the money out of the portfolio and see how much compound interest has been gained.
This is depicted in red in the following diagrams.
I use the cashback that the insurer offers. At the beginning of January I pay 96% of 12 monthly rates and put the remaining 4% on my savings account. I could get 0.001% on my personal savings account or 0.2% on my credit card account. If I go for conservative mutual funds, I might be able to make 1%; so I will assume 1% for this calculation.
From my monthly salary I transfer a full monthly rate into the savings account. When the payment is due, I take out as much as I need and transfer this to the insurer.
This is depicted in blue.
Which one is going to give me the least insurance costs for five years?
All payments are done at the beginning of the month, interest is earned during the month. The plots show the situations early in the month: after payments but before interest.
The balance in the portfolio (blue) and the saving account (red) are depicted here:
One can see that in the savings account the 4% cashback are building up. One could even think of putting those into the long-term portfolio.
The financal advantage in each year is depicted here:
One can see that the cashback variant (red) saves you a little less than 20 EUR a year, but that will be predictable. Putting the money into the portfolio might give you 22 EUR if the funds do gain 6%. However, the compound interest will help you and so the savings will start to become bigger each year.
The calculation and the plots are made with R, you can download the script
It seems that self-investing the money is a better choice. This way I can always access the money if I need it. With the cashback, I might have to go into overdraft since I cannot get the money back from the insurance company. The interest there will be somewhere between 10% to 20% which is much higher than I could get from investing.
Either way, with an hourly rate of 20 EUR/hour, I have already spend more time thinking about this than I would get out of the correct decision within five years. The moral of the story is best expressed with this xkcd comic.