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What is a low interest rate worth?

I’m considering buying a new car. Becka and I have gotten by with one car for ten years, but now with us both working and both jobs too far away to walk to and no good public transit, we’re going to need a second car.
We test drive some Volkswagons this afternoon. I thought I remembered reading that they offered a special 1.2% financing rate. This is a classic sales technique : confuse the consumer. So what, exactly, is 1.2% financing worth?
Loans work over a period of time, at the end of which the principle owed is zero. The amount of the payment owed is a function of the initial value of the loan and the interest rate. If the interest rate is zero, then the payment is simply the initial value divided by the number of payments.
What is interesting about that is that the payment on a loan is a function of two inputs : Initial value and interest rate. Now I do not believe that the car dealer has access to a pool of money at a lower interest rate than everyone else. When they sell you a car, they secretly “contribute” to your loan to make the interest rate lower. They in effect sell you the car for less than you agreed upon — but don’t ever tell you this.
Why should we care? Well, for one thing, you’re paying more taxes than you need to. But the reason I really care is that we might be able to buy our car with either separate financing (through an independent lender) or with cash. In that situation, you really want to know what the present value of the loan at the discounted interest rate is really worth.
This is one situation where Excel is useful. First I studied how interest rate affects payments. For typical car interest rates (between zero and 6 percent), the payment seems to correlate more or less linearly with the interest rate. That’s nice because it means I can make an assumption that simplifies my next calculation. Which is:
=PV((2+E$28)/1200,72,PMT(2/1200,72,$D29))
Where cell E$28 contains the “MSRP”, or price you negotiated. And cell $D29 contains the difference in interest rate between what the car dealer is offering and what current interest rates really are, as quoted by your bank or the internet. Basically I use to financial functions to find out what the present value of a loan with such and such payments over six years is worth today at the real interest rate.
Download a printable version of this table

Table 1. How much
money the dealer is getting from the financing dept
Difference between the Car lot interest rate and
the bank’s interest rate
  0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5 6 6.5 7
18000 18000 17735 17475 17220 16971 16726 16486 16251 16021 15795 15573 15356 15143 14934 14730
18250 18250 17981 17718 17459 17206 16958 16715 16477 16243 16014 15790 15569 15353 15142 14934
18500 18500 18227 17960 17699 17442 17191 16944 16702 16466 16233 16006 15783 15564 15349 15139
18750 18750 18474 18203 17938 17678 17423 17173 16928 16688 16453 16222 15996 15774 15557 15343
19000 19000 18720 18446 18177 17913 17655 17402 17154 16911 16672 16438 16209 15984 15764 15548
19250 19250 18966 18688 18416 18149 17887 17631 17380 17133 16892 16655 16422 16195 15971 15752
19500 19500 19213 18931 18655 18385 18120 17860 17605 17356 17111 16871 16636 16405 16179 15957
19750 19750 19459 19174 18894 18621 18352 18089 17831 17578 17330 17087 16849 16615 16386 16162
20000 20000 19705 19417 19134 18856 18584 18318 18057 17801 17550 17304 17062 16826 16594 16366
20250 20250 19952 19659 19373 19092 18817 18547 18282 18023 17769 17520 17276 17036 16801 16571
20500 20500 20198 19902 19612 19328 19049 18776 18508 18246 17988 17736 17489 17246 17009 16775
20750 20750 20444 20145 19851 19563 19281 19005 18734 18468 18208 17952 17702 17457 17216 16980
21000 21000 20691 20387 20090 19799 19514 19234 18960 18691 18427 18169 17915 17667 17423 17184
21250 21250 20937 20630 20329 20035 19746 19463 19185 18913 18647 18385 18129 17877 17631 17389
21500 21500 21183 20873 20569 20270 19978 19692 19411 19136 18866 18601 18342 18088 17838 17594
21750 21750 21430 21116 20808 20506 20211 19921 19637 19358 19085 18818 18555 18298 18046 17798
22000 22000 21676 21358 21047 20742 20443 20150 19862 19581 19305 19034 18769 18508 18253 18003
22250 22250 21922 21601 21286 20978 20675 20379 20088 19803 19524 19250 18982 18719 18460 18207
22500 22500 22168 21844 21525 21213 20907 20608 20314 20026 19743 19467 19195 18929 18668 18412
22750 22750 22415 22086 21764 21449 21140 20837 20540 20248 19963 19683 19408 19139 18875 18617
Text Box: MSRP

 23000 23000 22661 22329 22004 21685 21372 21066 20765 20471 20182 19899 19622 19350 19083 18821
23250 23250 22907 22572 22243 21920 21604 21295 20991 20693 20401 20115 19835 19560 19290 19026
23500 23500 23154 22814 22482 22156 21837 21524 21217 20916 20621 20332 20048 19770 19498 19230
23750 23750 23400 23057 22721 22392 22069 21753 21442 21138 20840 20548 20261 19981 19705 19435
24000 24000 23646 23300 22960 22627 22301 21982 21668 21361 21060 20764 20475 20191 19912 19639
24250 24250 23893 23543 23199 22863 22534 22210 21894 21583 21279 20981 20688 20401 20120 19844
24500 24500 24139 23785 23439 23099 22766 22439 22119 21806 21498 21197 20901 20611 20327 20049
24750 24750 24385 24028 23678 23335 22998 22668 22345 22028 21718 21413 21115 20822 20535 20253
25000 25000 24632 24271 23917 23570 23230 22897 22571 22251 21937 21629 21328 21032 20742 20458
25250 25250 24878 24513 24156 23806 23463 23126 22797 22473 22156 21846 21541 21242 20950 20662
25500 25500 25124 24756 24395 24042 23695 23355 23022 22696 22376 22062 21754 21453 21157 20867
25750 25750 25371 24999 24634 24277 23927 23584 23248 22918 22595 22278 21968 21663 21364 21071
26000 26000 25617 25242 24874 24513 24160 23813 23474 23141 22815 22495 22181 21873 21572 21276
26250 26250 25863 25484 25113 24749 24392 24042 23699 23363 23034 22711 22394 22084 21779 21481
26500 26500 26110 25727 25352 24984 24624 24271 23925 23586 23253 22927 22608 22294 21987 21685
26750 26750 26356 25970 25591 25220 24857 24500 24151 23808 23473 23144 22821 22504 22194 21890
27000 27000 26602 26212 25830 25456 25089 24729 24377 24031 23692 23360 23034 22715 22401 22094
27250 27250 26849 26455 26069 25692 25321 24958 24602 24253 23911 23576 23247 22925 22609 22299
27500 27500 27095 26698 26309 25927 25554 25187 24828 24476 24131 23792 23461 23135 22816 22503
27750 27750 27341 26940 26548 26163 25786 25416 25054 24698 24350 24009 23674 23346 23024 22708
28000 28000 27587 27183 26787 26399 26018 25645 25279 24921 24570 24225 23887 23556 23231 22913
28250 28250 27834 27426 27026 26634 26250 25874 25505 25143 24789 24441 24100 23766 23439 23117
28500 28500 28080 27669 27265 26870 26483 26103 25731 25366 25008 24658 24314 23977 23646 23322
28750 28750 28326 27911 27504 27106 26715 26332 25957 25588 25228 24874 24527 24187 23853 23526
29000 29000 28573 28154 27744 27342 26947 26561 26182 25811 25447 25090 24740 24397 24061 23731
29250 29250 28819 28397 27983 27577 27180 26790 26408 26034 25666 25306 24954 24608 24268 23936
29500 29500 29065 28639 28222 27813 27412 27019 26634 26256 25886 25523 25167 24818 24476 24140

For
example, you want to buy a car and negotiate the price to $21,750 with
dealer financing at 1.5%. The current bank interest rate is 6%. If you
pay cash, you should offer $19,085, as that is the present value of that
loan at the current interest rate.

One reply on “What is a low interest rate worth?”

Let me start by saying I work for a Credit union and up until February was part of their lending department, so I have a bit of insight on this. I think of it this way: they aren’t really lending you money — more like they’re lending you ownership of the car. It costs them less to have the car in your hands than taking up room on their lot AND they are getting the added benefit of that 1.2% (or whatever) in interest you are paying to them annually. It isn’t really Joe’s VW Sales that’s offering you that rate — it’s the Volkswagon Corp (or whatever they call themselves) who is financing your car — you’re buying it from the same people who are financing your loan so there isn’t any actual money changing hands at the time of sale. They’re actually making their money on the car itself, not the loan. A bank or other financial institution has to charge a bit higher rate because they make their money on the interest alone. I hope that all made sense — it’s so clear in my head!

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