Math Help - Basic Mortgage Math Question

I was using a Mortgage calculator that displays the steps used to arrive at the answer, but I have a question on one of the basic steps. It reads

You want the loan payment schedule for the following loan:

• Amount of the loan: $120000
• Duration of the loan: 30 years
• Payments per year: 12
• Annual interest rate: 4.5 %

Your annual interest rate converted to a decimal is 4.5% / 100.0 = 0.045.

• You will have 12 × 30 = 360 total payments to make.
• The interest rate at each payment is 0.05/12.00 = 0.0038.
• You can calculate the amount of each payment using this formula:

My question is where is this .05 value in the numerator coming from? How is it calculated? Once you obtain the .05 and complete the operation .05/12 that does not equal .0038 it equals .0042 (rounded up)

Thanks

The only thing I can think of is that they are rounding up the interest. The interest rate per month should be: (4.5%/yr)(1yr/12months) = 0.045/12 = 0.00375 = 0.375%. However, they have rounded up 4.5% to 5%, so that it is 0.05/12 = 0.0038. Hope that helps? Best of luck!

Thanks. I have an additional question as well, using different numbers this time.

Loan Amount $100,000
Interest 12%
Term 1 year
Monthly Payment $8,884.88

Using the excel formula PMT= (12%/12, 1*12, $100,000)

Monthly Interest = 12%/12 = .01
Total number of Payments= 1 * 12
Loan Amount= $100,000

To solve this they take the $100,000 + $6,618.55 = $106,618.55/12 = monthly payment of $8,884.88

My question is where does the $6,618.55 come from, and how is it calculated? I realize that $6,618.55 represents the total interest on the loan.

Thanks

So we can find the monthly payment by doing:
(r / (1 - (1 + r)^-N))P,
where r = monthly interest (.01), N = # of monthly payments (12) and P = initial amount (100,000):
(0.01/(1-(1+0.01)^(-12))*100,000 = 8884.88
Now this is our monthly payment there are 12 months so we multiply this by 12, which equals: 106,618.5464. Subtract 100,000 from this and we have: 6618.55.
I tried to find a more direct way to calculate this value, but that's the best I can do. I am not really a specialist on this sort of thing, but hopefully that will be sufficient? Really we just calculated the monthly payment and worked backwards from there. As I said a bit indirect, but it works?! Best of luck!

Oh, and these links may come in handy in the future:
Amortization Calculation Formula and Payment Calculator
$100000 loan at 12% for a year - Wolfram|Alpha

A = Amount borrowed
n = number of payments
i = periodic interest rate

Total interest = An[i / (1 - (1 + i)^-n)] - A

You can simplify by letting k = 1 - (1 + i)^-n) :
Total interest = A[(ni - k) / k]