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I want to apply for a mortgage loan of $100,000 with $10,000 down-payment. The loan should be paid in 15 years, and the interest rate is 4%. Suppose I can have $20,000 more by selling some of my stuff.

There is no prepayment penalty. Is there any significantly difference in the interest to pay between two cases:

  • Sell my stuff early, and have $30,000 down-payment.
  • Sell my stuff after a couple of months after closing the loan, then make a prepayment of $20,000.

I'm not good at numbers, and each bank has their own way of calculating APR, which makes me confused.


Updated: To clarify, I only want to minimize the interest that I have to pay.

  • The timing of the extra principal payment will determine how much it saves you, do you want to see calculations using 2-months post-close? – Hart CO Mar 16 '18 at 23:38
  • @HartCO: What I want to compare is with paying the principal after the loan vs increasing the down payment to reduce the loan. So we can assume 2 - 4-months post-close. – qsp Mar 17 '18 at 0:20
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    Don't forget PMI which might be required if you put down less than 20% – kweinert Mar 17 '18 at 0:42
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Plugging these numbers into mortgage calculator. 15 year term, 4% interest rate.

  1. $10,000 down payment, $90,000 loan, paying no extra principal: $666 monthly payment, $29,829 interest paid.

  2. $30,000 down payment, $70,000 loan, paying no extra principal: $518 monthly payment, $23,201 interest paid.

  3. $10,000 down payment, $90,000 loan, paying $20,000 of extra principal on the 3rd month of the loan term: $666 monthly payment, $16,628 interest paid, loan paid off in 131 months.

Option #1 is for reference of what would happen without the extra $20,000.

The question, the way I read it, is comparing options #2 and 3. Option #2 is to pay extra $20,000 upfront as part of down payment, whereas option #3 is to take out a bigger loan, and to include extra $20,000 of principal in the 3rd monthly payment.

As can be seen, the difference between #2 and 3 is substantial:

  • Option #3 has higher minimum monthly payment: $666 vs $518, an increase of $148.

  • Option #3 has shorter actual loan term: 131 months vs 180 months, a difference of 49 months.

  • Option #3 has lower lifetime interest paid: $16,628 vs. $23,201, a reduction of $6,573.

Analysis of the difference:

  • Taking out a bigger loan increases the minimum monthly payment.

  • Paying extra principal does not reduce the monthly payment - instead, it reduces the actual loan term.

  • Shorter actual loan term means lower lifetime interest paid.

Essentially, we are looking at a trade-off between minimum payment and the loan term / lifetime interest paid.

Finally, I would caution against getting too hung up on the lifetime interest amount. This number, while not meaningless, is not as important as it may seem. $100 now and $100 ten years later is not the same thing, and not just because of inflation. Extra flexibility that comes with lower monthly payment can go a long way in case of cash inflow becoming lower.

  • OP states loan of $100,000 with $10,000 down payment, so I think you need to adjust all up. – Hart CO Mar 16 '18 at 23:47
  • @void_ptr: Thanks. But this is counter-intuitive for me that prepayment is much better than increasing. May I ask what is the mortgage calculator that you are using? and does APR matter? – qsp Mar 16 '18 at 23:53
  • @HartCO Right, I misread OP's question originally. I think I got it right in my edit. – void_ptr Mar 16 '18 at 23:55
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    @qsp I added a bit of extra analysis on why is this difference, as well as my thoughts on which is better. – void_ptr Mar 17 '18 at 0:06
  • Another thing to consider is using all or some of the cash to "buy down" the interest rate, referred to as "buying points". – Norm Mar 19 '18 at 21:43
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I think you've got fine answers here, but thought the following might help, I assumed you meant a $110,000 house so my numbers are based on that. The big difference in your two scenarios is that as a down-payment the extra 20k would reduce your monthly payment significantly, while as an extra principal payment it reduces the loan duration significantly. You'll notice that putting 30k down but making payments at the 10k down payment rate is pretty comparable to making a 20k extra payment after 2 months.

Mortgage Scenario Comparison

As noted by others, when you are putting less than 20% down you'll be faced with private mortgage insurance (PMI) that adds extra cost until you have 22% equity (based on original appraised value), not super significant here given the plan to make the significant extra payment so early, but going for 20% down payment will save you a little money and a little hassle.

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It seems you meant a $100k loan not a $100k property, it takes too long to reformat so you can get the general idea from this table.

Here's a rough amortization table, showing a monthly breakdown of year one, A/B testing a $20,000 payment in Month 4. Typically interest is charged on the average daily balance of the principle as early as you can make payments, it has a cascading effect through the remainder of the loan. The $20,000 payment saves you about $12,700 over the life of the loan and completes the loan about 4 years early, assuming it's made on month 4. If it's made in month 8 or 29 it would have a lesser effect.

Here are the forumulas if you want to build yourself an Excel (or whatever) sheet.

1st month Principle = Plug this in

Interest = principle * (0.04/12)

Payment = pmt(0.04/12, 12*15, principle)

2nd and on Principle = Prior Month Principle + Prior Month Interest + Prior Month Payment

Once you have your sheet you can play with the numbers.

                       Principle    Int     Pmt     Principle    Int    Pmt

Month 1                 -90,000     -300    666     -90,000     -300    666
Month 2                 -89,634     -299    666     -89,634     -299    666
Month 3                 -89,267     -298    666     -89,267     -298    666
Month 4                 -88,899     -296    666     -88,899     -296    20,000
Month 5                 -88,530     -295    666     -69,196     -231    666
Month 6                 -88,159     -294    666     -68,760     -229    666
Month 7                 -87,787     -293    666     -68,324     -228    666
Month 8                 -87,414     -291    666     -67,886     -226    666
Month 9                 -87,040     -290    666     -67,447     -225    666
Month 10                -86,664     -289    666     -67,006     -223    666
Month 11                -86,287     -288    666     -66,563     -222    666
Month 12                -85,909     -286    666     -66,119     -220    666
Year 1 End Balance      -85,530                     -65,674     
Year 1 Int. & Pmt                   -3,519  7,989               -2,997  27,323

Year 2 End Balance      -80,878                     -60,213     
Year 2 Int. & Pmt                   -3,337  7,989               -2,528  7,989

Year 3 End Balance      -76,036                     -54,529     
Year 3 Int. & Pmt                   -3,147  7,989               -2,305  7,989

Year 4 End Balance      -70,997                     -48,614     
Year 4 Int. & Pmt                   -2,950  7,989               -2,074  7,989

Year 5 End Balance      -65,753                     -42,458     
Year 5 Int. & Pmt                   -2,744  7,989               -1,833  7,989

Year 6 End Balance      -60,295                     -36,051     
Year 6 Int. & Pmt                   -2,531  7,989               -1,582  7,989

Year 7 End Balance      -54,615                     -29,383     
Year 7 Int. & Pmt                   -2,308  7,989               -1,321  7,989

Year 8 End Balance      -48,704                     -22,444     
Year 8 Int. & Pmt                   -2,077  7,989               -1,049  7,989

Year 9 End Balance      -42,551                     -15,221     
Year 9 Int. & Pmt                   -1,836  7,989               -766    7,989

Year 10 End Balance     -36,148                     -7,705      
Year 10 Int. & Pmt                  -1,585  7,989               -472    7,989

Year 11 End Balance     -29,484                     0       
Year 11 Int. & Pmt                  -1,325  7,989               -166    7,871

Year 12 End Balance     -22,548                     
Year 12 Int. & Pmt                  -1,053  7,989               

Year 13 End Balance     -15,330                     
Year 13 Int. & Pmt                  -771    7,989               

Year 14 End Balance     -7,818                      
Year 14 Int. & Pmt                  -476    7,989               

Year 15 End Balance     0                       
Year 15 Int. & Pmt                  -170    7,989               

Grand Interest& Payments         -29,829  119,829           17,091       107,091
  • Doesn’t a sub-20% down payment require PMI? That would change the numbers. – JoeTaxpayer Mar 17 '18 at 0:00
  • @JoeTaxpayer True, but just a couple months of PMI. – Hart CO Mar 17 '18 at 0:00
  • @HartCO well it would be like 2 years before there was 20% equity, but again, not worth redoing the formatting, I'd rather just delete the answer lol... This gets the general idea of the cascade effect of paying principle early. – quid Mar 17 '18 at 0:02
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    OP will not remove PMI until the natural amortization puts him at 80% LTV. Not worth it to put 10% down if one has such an aggressive prepayment plan. Just save to 20% – JoeTaxpayer Mar 17 '18 at 0:09
  • @quid: thanks for the answer. I understand paying principal early is better, but how it compare to include it as part of the down-payment to reduce the loan? – qsp Mar 17 '18 at 0:14
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Leaving aside the purely numerical calculations of the other answers, you might find there are other benefits of making a 30% down payment rather than 10%.

  • Larger down payments often attract better interest rates than smaller ones.

  • A larger down payment might remove your requirement to buy mortgage protection insurance

  • A larger down payment can make more lenders interested in lending to you resulting in more competition and better rates.

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