# Help calculating mortgage payments?

How would I calculate this.. I already know it's 630/mth, but how do I caluclate it?

What would be the monthly payment on a $90,000 mortgage at a rate of 7.5% interest for 30 years?

I actually need a formula.. not a loan calculator..thanks.

### 6 Answers

- linkus86Lv 71 decade agoBest Answer
A formula exists on wikipedia (see link below) but beware there is a reason why these types of calculations are best done on a calculator

- 1 decade ago
M = P [ i(1 + i)n ] / [ (1 + i)n - 1]

Where M is the monthly payment. i = r/12. The same formula can be expressed many different way, but this one avoids using negative exponentials which confuse some calculators.

For our $100,000 mortgage at 5% compounded monthly for 15 years, we would first solve for i as

i = 0.05 / 12 = 0.004167 and n as 12 x 15 = 180 monthly payments

Next we would solve for (1 + i)n = (1.004167)180 using the xy key on the calculator, which yields 2.11383

Now our formula reads M = P [ i(2.11383)] / [ 2.11383- 1] which simplifies to

M = P [.004167 x 2.11383] / 1.11383 or

M = $100,000 x 0.00791 = $791.81

Source(s): http://www.fonerbooks.com/interest.htm - Anonymous1 decade ago
you must be living in us which the following formula is applicable:

m1=12 monthly compounding (in us), in canada m1=2

m2=12 monthly payment made at the end of each compounding period

YR=30 no. of years amortized

n = no. of payments

n = (m2) * (YR)

n = 12 * 30 = 360

int = interest adjusted to account for compounding

int = (%int) / (m1) / (100)

int = 7.5%

int = (7.5) / 12 /100 = 0.00625

INT = interest adjusted to account for monthly payment

INT = (1 + int) ^ (m1 / m2) - 1

INT = (1 + 0.00625) ^ (12 / 12) - 1

INT = 0.00625

PV= outstanding loan = 90,000

F1 = interest portion of monthly payment

F1 = (PV) * (INT)

F! = 90000 * 0.00625 = 562.50

F2 = monthly equal payment factor

F2 = 1 - (1 + INT) ^ ( - n )

F2 = 1 - (1 + 0.00625) ^ ( - 360) = 0.89386017074

PMT = monthly equal payment

PMT = F1 / F2

PMT = 562.50 / 0.89386017074 = 629.29

the bank round this to $630/mth

- 1 decade ago
First tell me you are not paying 7.5% on a 30 yr fixed rate loan! The going rate today is 5.875%. Go back to who ever is over charging you get a better rate. FYI at 7.5% the payment is $629.29 and at 5.875% it is 532.38, almost $100.00 if you get the $532.38 payment and pay the $629.29 payment you will pay off the 30 yr loan in 20 years and save over $34,000! Cool, hah? Fight for a great rate! Watch out for the insurance and taxes, you need to be aware of all of the housing expenses!

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- Spock (rhp)Lv 71 decade ago
bankrate.com ... look for their mortgage calculator -- middle leftish of page about fourth or fifth one down

Source(s): 8-)