# Is there any difference in paying upfront versus in monthly installments?

So let's assume I wanted to rent a house which has monthly rent e.g 300 euro every month starting at 1/1/2010.

And let's assume I wanted to rent this house for 24 months.

Only in terms of inflation

Would it be better for me to pay at 1/1/2010 7200 euro (24*300)?

Or would it I lose less value if I just paid 300 euro every month till the end of 2012?

Or is it the same?

In other words how to calculate inflation per month?

I use this website to get the results for different months http://fxtop.com/en/inflation-calculator.php

For example When just use 7200 euro as an input for 1/1/2010 (using EUCPI2005 as an index) I get 7561.75 as a result for 1/1/2012.

Now to calculate the difference in monthly payments of 300 euro using the above webpage what should I do?

Should I have 300 euros of 1/1/2010 as the reference, add the 1/1/2010 to 1/2/2010 result to my initial 300 euro, add the 1/1/2010 to 1/3/2010 result to the sum of my initial 300 euros + the result for February + this result and so on?

Only in terms of inflation

Because of inflation, €300 would be worth less in December 2011 than it was in January 2010. Thus, it's to your benefit to pay in monthly installments rather than up-front.

Now to calculate the difference in monthly payments of 300 euro using the above webpage what should I do?

You'd need to calculate 23 different values:

• Jan 2010 -> Feb 2010
• Jan 2010 -> March 2010
• Jan 2010 -> Apr 2010
• etc, etc
• Jan 2010 -> Novem 2011
• Jan 2010 -> Decem 2010

But this is a pointless exercise, since you'd have signed a 24 month lease at a fixed price. Hence, my original comment.

If given the option of up front or monthly, here are some scenarios where it would be beneficial to pay the lease up front instead of monthly (neither of which are affected by inflation):

1. If you receive a discount for paying up front. Some landlords are happy to receive a year or more worth of rent up front, and will reduce the overall price as a result. (e.g. perhaps only charge 11 months instead of 12.)
2. If you keep your money in the bank with negative interest rates. AFAIK the US has never had negative interest rates (though extremely low rates with a monthly banking fee could be thought of as a negative return), but some countries (Japan is one) have recently been utilizing negative interest rates to fight against deflation.

Barring the above scenarios or some reason you don't want to keep money around (such as if you have some sort of addiction causing you to spend money, or you have an imminent lawsuit which will take all of your money), you are better off paying monthly.

Inflation will hurt your landlord, but it won't hurt you. In either case, you have to pay 7200, regardless of how much inflation has increased over two years.

However, they are not equivalent to you. If you take the monthly payment, then you can potentially come out ahead. If you were to take the 7200 and put it in a savings account and just pay monthly then you'll be earning interest that you wouldn't get if you paid up front.

There's a whole lot of other investment options you could go with too, but that's another question. The risk here is that if you go through financial hardship you may be tempted to draw on that 7200 early and come up short for rent one month.

• Compound rates/stockmarkets/investments etc do not interest me in this particular question I want only to focus on inflation and nothing else. and yes it will hurt me since if I pay 7200 upfront now I would lose value because it means that it would be the same deal as paying ~7500 euro at the end of the two years. Or in other words paying 7200 now will add buying power to my landlord and not hurt him. Oct 19, 2017 at 12:41
• If you had 7200 in cash o 1/1/2010 which you put in a box under your bed, then it wouldn't matter to you whether you emptied your box completely on 1/1/2010 or in small amounts over the next two years. Either way you would have an empty box. If you paid out small amounts and invested that money somehow, then you could come out with some money leftover in the box at 1/1/2012. Oct 19, 2017 at 12:49
• Oh come on dude dont try to exploit irrelevant details of a theoretical example... the focus of the question is which calculation (involving only inflation as a variable) would lead to a smaller number at 1/1/2012 (or in other words bigger value).And if it is so hard not to imagine me having a box under my bed for 2 years filled with money then assume 2 different people in parallel dimensions one that spends 7200 upfront and an other guy that just has 300 each month...both dimensions have the same dates and everything else is the same who will end up with a better deal for the house @1/1/2012? Oct 19, 2017 at 13:28
• The answer is the same: inflation doesn't matter for the tenant Oct 19, 2017 at 13:55
• @papajo : No, it's not indisputable. We are disputing it. Oct 19, 2017 at 16:24

Inflation is not applicable in the said example.

You are better off paying 300 every month as the balance when invested will return you income.

• Why is inflation not applicable? If I pay 7200 upfront it would be like paying 7500 at the end of the lease. Also for investing and income compound rates etc are irrelevant to my question since I want to only analyze this under the context of inflation. Oct 19, 2017 at 12:38
• 7200 dollars in today's money could easily be worth more in a year, not likely to be much, but something, so inflation seems applicable to me. Oct 19, 2017 at 13:25
• @papajo read my answer as to why inflation is not applicable. money.stackexchange.com/a/86297/22266 Oct 19, 2017 at 14:29
• @papajo Inflation means more money buy same thing. In your example the rent is constant and hence there is no inflation. Oct 19, 2017 at 16:00

### Investment vs. purchase

You can use the 6900 to make an investment. Or to buy something. That's why people keep reminding you that you could make interest. Because most people think of either 7200 now or paying the same 7200 over time. So you could just be storing the 7200 under the mattress until you pay it out. Obviously in that case, inflation doesn't matter ("is not applicable"). You've given up the use of the 7200 from the beginning.

Think of it instead as 7200 now and twenty-three payments of 300 each. So 14,100 total. Then you can spend 6900 on something else at the beginning or spend 300 a month on other things. The difference between spending 6900 now and 300 in each of twenty-three months would be measured in inflation. Of course, this requires you to have both 7200 now and an income stream producing at least 300 a month.

Another way of doing things is to take 6900 and invest it. Each month you remove 300 and use it to make a payment. We're now back to just one 7200, plus the interest over time. I would argue that this is still an inflation advantage. It's just that instead of spending the money, you invested it. And that of course is your prerogative. The point being that you would not have that opportunity if you paid up front.

### Calculation

Now to calculate the difference in monthly payments of 300 euro using the above webpage what should I do?

As already said, you would have to calculate twenty-three values and then sum them with the 300 you pay up front in the monthly.

There are other ways to calculate it, if you are not using that particular tool. For example, there are formulas to calculate the net present value of an annuity. E.g. see Investopedia.

``````P = PMT x ((1 - (1 / (1 + r) ^ n)) / r)
``````

Where:

`P` = the present value of an annuity stream

`PMT` = the dollar amount of each annuity payment

`r` = the inflation rate

`n` = the number of periods in which payments will be made

Investopedia talks about interest rates, but you can put inflation there for this purpose. In that case, `r` might better be called the "discount rate".

`PMT` is 300.
`r` is whatever estimate you are using for inflation. E.g. .003 per period.
`n` is 23.

Note that the monthly inflation rate is smaller than the annual rate. So .003 is about 3.66% annually. 3.04% annually is more like .0025 a month.

I found calculators for this with search terms "present value of annuity calculator". Some of the calculators will take the annual rate (3.66%) and number of periods per year as input. Or the calculator may take a monthly rate as a percentage (.3%) rather than as a decimal (.003). So be careful of the inputs.

This gives me a net present value (NPV) of 6,657.69 for the 23 payments of 300, assuming .3%. Or 6957.69 is the NPV of the monthly payments and 7200 is the NPV of the 7200 up front.

### Other considerations

Obviously if you can pay less than 6957.69 up front rather than 7200, then it makes more sense to pay up front.

Even without a discount though, it still may make more sense to pay up front.

1. You can't spend the money in the meantime, so you manage yourself better.
2. Real (inflation-adjusted) interest rates are often negative for small amounts.
3. You may not have the 300 per month surplus income to keep up with the payments.
4. Avoid fees if you miss a payment.

How much those intangibles are worth is up to you.