Assuming there is no fees on paying extra $10k at the time of the first scheduled mortgage payment, what would be better - to put this $10k towards a downpayment or make bigger regular payment?
Maybe someone can show me online calculator where I can calculate the difference at the end?
This calculator will let you calculate the savings from making a prepayment right away. Run it twice: once with a smaller initial balance, and once with the high balance and the prepayment.
If you add the extra $10k to your down payment, your monthly payment will be lower. The higher monthly payment you will have with the $10k in your first payment means that you'll be paying more principal every month, right from the beginning.
Using the calculator above with a $200k mortgage at 5% fixed for 30y: if you use the $10k as a prepayment, you'll save about $22k in interest over the life of the loan, which will be shortened by 38 months. Bottom line: don't put it into the down payment. But also see KeithB's answer for the trade-off here.
That's assuming a US mortgage, which is different from Canada. I ran the same numbers using this calculator from RBC and came up roughly the same amount. (I find the first calculator above much easier to use, if you aren't worried about losing a little precision in the numbers.)
They should come out just about equal, assuming that you make the same monthly payment in both cases. Using the Calculator @bstpierre mentioned, the monthly payment for a $100k loan at 4% for 20 years is $604. If you had a $90k loan, the payments would be $543. If you pay $604/month on the second loan, putting the extra towards principal, it would work out about the same as paying an extra $10k with the first payment on the first loan. The advantage of the second loan is that you can always pay the $543 if necessary due to unforeseen circumstances. If you have the discipline to make the higher payments, I would include the extra money in the first payment. If you think you might be tempted to cut back on the payment sometime in the future, put the extra money towards the downpayment.
This question carries the risk of comparing apples and oranges. Having said that, one way to make a comparison is described below. First, I would suggest you download the Free Canadian Mortgage Calculator by Vertex42.
In the example, let's say your purchase price was $100000, your current downpayment was $10000, and you take a mortgage at 7% amortized over 25 years. The two options in your question would be decided by either changing the downpayment to $20000 or putting a $10000 additional payment in cell E34.
By making the additional payment, you save a lot of interest only because the monthly payment remains the same. Thus, more of each monthly payment would be applied to your principal balance after your huge additional payment in the first month. Also, your amortization becomes shorter.
On the other hand, increasing your downpayment decreases your total monthly payment given the same 25 year amortization. The interest you pay is higher in this case.
With awareness that this question is many years old, it bears mentioning that the other answers all essentially assume that the loans are equivalent on all terms aside from the down payment (and impact to monthly payments as a result of a different down payment). It's important to note that this may not be the case. It would be somewhat rare for a 10% difference in down payment to have zero affect on loan terms for most typical mortgages.
Lenders consider many factors when writing a mortgage, and they have many variables to adjust for different scenarios. The size of your down payment can have a significant impact on the terms of the loan. Lenders generally like to see larger down payments from a risk perspective (a larger down payment means a safer loan to value ratio). As such, it's often the case that the mortgage products with the best terms have higher down payment requirements - for instance, the lender's best rates may only be available if you put 20% or more down up front. So, putting more money down may in fact mean that your loan is written at a better interest rate.
Additionally, many lenders will have personal mortgage insurance requirements (known as CMHC in Canada or PMI in the US) based strictly on down payment size. In Canada, if your down payment is less than 20%, the lender is required to book CMHC on the loan - so even though the finances of the loan itself won't be different in terms of principal and interest payments, if that 10% extra cash would have brought you above the 20% threshold, you would see significantly different monthly payments (because you wouldn't be carrying the insurance).
All that said - if your loan would be 100% the same regardless of you putting that extra 10% down up front vs adding it to your first payment, then the other answers are relevant. However, it's important to understand the big picture in terms of all terms of the loan, before making this sort of decision. If you're already working with a bank or a mortgage agent, they can likely explain the difference for you and show you the actual numbers, which should make the decision easy.
