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%.