Increasing downpayment v.s. Prepayment

Question

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.

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

Answer 1

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.

Answer 2

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.

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.

Answer 3

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

Answer 4

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.