Calculations of a 15 years v 30 years mortgage.

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Galego

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Hi,
I am doing some finance calculations about how much more a 30 yrs mortgage costs you over a 15 yrs mortgage. This example takes into account the principle that one dollar today is worthier than one dollar tomorrow.

My example is in an amount of 250k and take the assumption of a 5% fixed interest for the 30 years.

Summary of the two mortgages:

15yrs - monthly rpymt = [FONT=&quot]1,976.98 eur[/FONT]
30 yrs - monthly rpymt = [FONT=&quot]1,342.05 eur[/FONT]

15yrs - annual rpymt = [FONT=&quot][FONT=&quot]23,723.76 [/FONT] eur[/FONT]
30 yrs - annual rpymt = [FONT=&quot][FONT=&quot]16,104.60 [/FONT] eur[/FONT]

Annual difference = [FONT=&quot]7,619.16 eur

[/FONT]15yrs - total rpymt = [FONT=&quot][FONT=&quot]355,856.40 [/FONT] eur[/FONT]
30 yrs - total rpymt = [FONT=&quot][FONT=&quot]483,138.00 [/FONT]eur[/FONT]

Total difference = [FONT=&quot][FONT=&quot]127,281.60 [/FONT] eur[/FONT]

So now I took the annual extra 7.6k cash and put it in a deposit which pays a 3% APR; compounded it for 30 years. I also did the same with the 23,723 eur, which you will not need to pay any longer once the 15 yrs mortgage has been paid off, and again put in a 3% APR; compounded it for 15 years.
These are the amounts which I got:

15 yrs = 454,473.25 eur
30 yrs = 373,359.25 eur

Finally, I calculated the Net Present Values for those above amounts using a 5% opportunity cost (30 years).

15 yrs = 105,154.86 eur
30 yrs = 86,386.91 eur

Difference = 18,767.95 eur


So if my calculations are correct, 18k eur are the real savings between a 15 yrs vs 30 yrs mortgage. This amount is based on the assumption stated in my above example.


I am open to correction. I’d love to know if I have got it right.
 
No tax implications in this example (no DIRT, no MIR, etc).

The biggest factor in a mortgage life is possibly the inflation and the huge role which this plays over 15 and 30 years.
 
Hi Gaelgo

I am not really sure what the point of your calculations is?

If I rent a car for two weeks, it will be twice the price of renting a car for one week.

If I rent money for 30 years, it will be twice the cost of renting it for 15 years.

You should only look at interest on an annual or other period basis. The rate of interest is 5%. If you borrow it for one year, it will cost you €500. If you borrow it for two years it will cost you c. €1,000.

Renting money is expensive.

Likewise if you put money on deposit, you are hiring it out and you are getting interest paid on it. If you put it on deposit for 2 years, you will get twice what you get for hiring it out for one year.
 
Brendan Burgess said:
Hi Gaelgo

I am not really sure what the point of your calculations is?
Click to expand...

Hi Brendan,

My point is that a 30 years mortgage does not cost the double than a 15 years mortgage. In fact, someone may argue that you could be better off in a 30 years mortgage than a 15 years mortgage.

Using the same amount of money in both cases (15 v 30) and calculating the Net Present Values in both examples after 30 years, the difference is only 18k eur. My example assumes a flat, constant inflation throughout the 30 years. Of course, this has not been historically the case and looking at the irish inflation in the last 30 years, it has certainly been nothing like flat or constant.

Borrowing large amounts in long period may, in certain cases, be better than paying them off sooner. As I said in my previous post, a dollar today is worth more than a dollar tomorrow.
 
Hi Gaelgo

As I said, you pay an annual rent for money. The longer you rent it, the more you pay. That really is the best way to look at it.

You are making a very complex comparison which complicates matters. After 15 years of a 30 year mortgage, you will have paid off a good lump of the mortgage. So you are not borrowing €250k for 30 years. You are constantly paying it down.

If people could only understand that interest is the rent paid for renting money, they would think much more clearly on a lot of issues.
 
I know what you saying Brendan but I also get the other man's point of view.
On a 15 versus 30 year mortgage the 30 year mortgage may be more affordable than the 15 year mortgage, because it's much less money every month.
I know you will pay more interest in the long run.
Also one could pay back a 30 year mortgage in 15 years if they had the resources. But it would be more difficult to pay back a 15 year mortgage in 30 years.
 
Hi Richie

I have been a big fan of borrowing over as long a term as possible. I have been criticised for recommending interest only mortgages which, is the longest possible term.

But the beauty of them is that a borrower can repay the capital when it suits them.

The "more interest in the long term" makes no sense to me.

Brendan
 
Brendan Burgess said:
Hi Gaelgo

As I said, you pay an annual rent for money. The longer you rent it, the more you pay. That really is the best way to look at it.

You are making a very complex comparison which complicates matters. After 15 years of a 30 year mortgage, you will have paid off a good lump of the mortgage. So you are not borrowing €250k for 30 years. You are constantly paying it down.

If people could only understand that interest is the rent paid for renting money, they would think much more clearly on a lot of issues.
Click to expand...

Hi Brendan,

Sorry, my intention was not to over-complicate things but to introduce the concept of Net Present Value - today's value of money of future amounts , and the role and impact of inflation in a mortgage.

My point is not about the interest in a 15 or 30 years mortgage, it is about the wearing down of the value of money in the long term (not sure if this makes sense). In my view, the value of having the extra 7k (like in my example) is more valuable today than to pay off future debts.

Hope I am bringing my point across well.
 
I also think you are over complicating this. I think your calcs are OK and reasonably realistic, though you have not explained or justified your choice of discount rate. The rationale behind the choice of discount rate is key to your conclusion.

The only practical situation in which it is applicable is where someone has the means to pay off their mortgage earlier or place their money on deposit. It is quite obvious (and covered extensively in other threads) that this is dependent on the relationship between the rate at which you have borrowed versus the deposit rates available.

The other point you are making is quite true. Many people would look at the difference in total cost of credit (€127k in this case). This number means practically nothing unless you foolishly believe someone should lend you money for free (i.e. no interest charged).
 
Galego said:
Hi Brendan,

Sorry, my intention was not to over-complicate things but to introduce the concept of Net Present Value - today's value of money of future amounts , and the role and impact of inflation in a mortgage.

My point is not about the interest in a 15 or 30 years mortgage, it is about the wearing down of the value of money in the long term (not sure if this makes sense). In my view, the value of having the extra 7k (like in my example) is more valuable today than to pay off future debts.

Hope I am bringing my point across well.
Click to expand...

How can you over complicate the biggest financial decision of your life? (i.e. ignore Brendan) Excellent analysis. Others should sit down and do the hard maths.

Quotes like the below from Brendan are nuts. Obviously you can get higher deposit returns if you lock up your money for longer.

'If you put it on deposit for 2 years, you will get twice what you get for hiring it out for one year.'

It's like maths for kids.
 
The thing is there is no point in saving the extra €7619 per annum if you are on the 30 year mortgage (unless you are saving it for emergencies or whatever). You are borrowing at 5% and your savings are earning you 3%. If you were willing to save that €7619 per annum it would be better to put it towards the mortgage as it would work out cheaper. Of course if you do that you'll pay it off in the 15 years any way.
 
At the moment we all agree it is good to pay down debt fast, especially when the interest rate charged is higher than our after tax return with cash.

BUT I still think it is a very interesting idea to try and calculate the npv of paying your mortgage over a shorter term. my intuition told me it was worth more than your calculation demonstrated.

BUT I think you are drawing a large conclusion from some fixed starting figures.

I think you would need to redo the calculations with a range of possible starting figures and see how much the conclusion changes.

At a minimum for a second iteration I would suggest a discount rate should be 3%. (given current inflation and deposit rates might be more realistic). and reduce the deposit rate to 1.75% or so to take effect of DIRT.

I would also like to see the figures for mortgage interest rate of 2.5% and 7%.
 
Talk about knowing the price of everything and the value of nothing. Above brought that to mind. Though fantastic but pointless analysis.In a 'perfect theoretical' world the correct discount rate applied to future cash flows should bring you back to today's value by definition.
In other words, in plain English in the above case if interest rate charged is higher than net after tax interest received it can never make financial sense to save instead of paying debt. Paying debt will always save.
If you play around with figures of course you can prove anything. And so say 76% of people. The other 56% don't have an opinion. Statistics and numbers!
 
Better off getting the 30 year mortgage and overpaying to make it the same as 15 years.
Then if you fall on hard times you can go back to the 30 year schedule and pay lower amount back at no extra charge or restructuring.
 
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