0

I'm currently deciding between taking loan with down payment and no down payment. To get behind the idea, I read a case study from a finance textbook.

I get the basic math and understand concept of present value, but couldn't understand how some numbers came up while analysing it. Here is the case:


Mortgage loan is $100,000, with 30-year duration. You can choose either to pay down payment or not. If you don't, annual interest rate is 12%, if you do take the offer of paying $2,000 (2% discount point off initial $100,000), you get 11.5% annual interest rate.

Case 1. No down payment, annual interest rate is 12%, therefore, monthly is 12%/12 = 1%. Compounding monthly:

Effective annual rate =  (1.01)^12 - 1 = 0.1268, which is = 12.68%

Case 2. Down payment = $2,000. (so, now we owe $100,000-$2,000 = $98,000) Interest rate at 11.5%, therefore, monthly should be 11.5%/12 = 0.9583%.

In this case, using finance calculator, monthly payment would be $990.29

Now, this is where the confusion begins. My monthly rate as what I manually calculated is 0.9583%, BUT the book states it should be 0.9804%.


Hence, Question: How and why does the monthly rate turn out to be 0.9804%??

If we reverse the calculation with that rate, it turns out we actually get higher interest rate; 0.9804% * 12 = 11.76%, higher than initial 11.5%.

Quote/screenshot from the book: enter image description here enter image description here

  • 4
    The 2 'points' for which you pay 2000$ will buy you the lower interest rate. They are not a down payment, you still owe the full amount. – Aganju Aug 19 '17 at 13:56
  • @Aganju thanks for the comment. Agreed. I misunderstood the concept. Feel free to edit my question. That being said, how would the calculation using 'points' affect the interest rate? As you can see, the book suggest 0.9804%. That's 11.76% annual. Higher than what I would be paying at 11.5% (0.9583%).. – Mr. Slow Aug 19 '17 at 14:25
  • The 2K is interest. If you payoff the loan before the breakeven point the interest rate is very high. But it will always be larger then 11.5% – mhoran_psprep Aug 19 '17 at 17:14
  • The image shows a footnote 1 after the 0.9804% figure: does that say anything relevant? – TripeHound Aug 21 '17 at 6:52
3

With the $2000 downpayment and interest rate of 11.5% nominal compounded monthly the monthly payments would be $970.49

As you state, that is a monthly rate of 0.9583%

Edit

With the new information, taking the standard loan equation

s = (d - d (1 + r)^-n)/r

where

s is the loan principal
d is the periodic payment
r is the periodic interest rate
n is the number of periods

Let

s = 100000
r = 0.115/12 = 0.00958333
n = 30*12 = 360

d = (r (1 + r)^n s)/((1 + r)^n - 1) = 990.291

Now setting s = 98000, with d = 990.291 solve for r

r = 0.980354 %

enter image description here

  • yes. But in the book, it states that the monthly rate is 0.9804%. Wondering if I missed something the textbook assumed. – Mr. Slow Aug 19 '17 at 9:01
  • @Mr.Slow Can you quote more of the book, or include an image, because that rate seems unrelated to anything else you're mentioned. – Chris Degnen Aug 19 '17 at 10:44
  • hey Chris, up there, I uploaded the screenshot of the case. second paragraph from the bottom. – Mr. Slow Aug 19 '17 at 11:53
  • 2
    Hey Chris, just a thought for you. There is no down payment. The $2000 is "points". To the OP - points or money paid to the bank or lender in exchange for a bit of a lower interest rate on the loan. I will let Chris take it from here – JoeTaxpayer Aug 19 '17 at 12:25
  • @JoeTaxpayer, My bad, you're right, just realised they are points which means in both cases actually there are no money down. However, wouldn't the rates be unaffected? I believe that monthly rate should be 0.9583% (11.5% annual)? If you look at the screenshot, the book suggest higher interest rate, 0.9804% (11.76%). How does it get to that number? – Mr. Slow Aug 19 '17 at 14:21

Your Answer

By clicking "Post Your Answer", you acknowledge that you have read our updated terms of service, privacy policy and cookie policy, and that your continued use of the website is subject to these policies.

Not the answer you're looking for? Browse other questions tagged or ask your own question.