How do you calculate a mortgage payment?

You can follow Captain what's his name above - and be totally bonkers in the brain, along with me, or "you" don't calculate it. The lender does, and tells you what the payments will be. Be prepared to pay $300 or $400 more than what they tell you because when the papers come back - they lie.

https://www.moneysavingexpert.com/mortgages/mortga...

The basic payment is going to be principal + interest. The formula for generating that is built from a geometric sum. Some mortgages handle insurance, property tax, HOA fees (if applicable) and other fees associated with owning a home. Some don't and tell the borrower that they're responsible for handling those fees.

Basic payment, principal and interest. If we construct a 3-payment plan, we can generalize it to an n-payment plan.

You receive a loan of L and you make a payment of P. You have a fixed annual interest rate of i (which is divided by 100, so if you have a 5% interest rate, then i = 0.05) and you make 12 payments per year

First, add the accumulated interest to the loan amount.

L + L * (i/12) =>

L * (1 + i/12)

Subtract a payment of P

L * (1 + i/12) - P

This will give you the remaining balance that you owe. Add interest again

(L * (1 + i/12) - P) * (1 + i/12)

Subtract a payment of P

(L * (1 + i/12) - P) * (1 + i/12) - P

Do the process again

((L * (1 + i/12) - P) * (1 + i/12) - P) * (1 + i/12) - P

Let 1 + i/12 = k, just to clean things up

((Lk - P) * k - P) * k - P

If we say that this equals some amount R, then we can solve for L

((Lk - P) * k - P) * k - P = R

((Lk - P) * k - P) * k = P + R

(Lk - P) * k - P = P/k + R/k

(Lk - P) * k = P + P/k + R/k

Lk - P = P/k + P/k^2 + R/k^2

Lk = P + P/k + P/k^2 + R/k^2

L = P/k + P/k^2 + P/k^3 + R/k^3

Can you see how we can extend this to an n-number of payments?

L = P/k + P/k^2 + P/k^3 + ... + P/k^n + R/k^n

This tells us what our original loan amount is, what our payments are, and what the remaining principal is after n payments.

What we need now is some way to condense P/k + P/k^2 + P/k^3 + ... + P/k^n

S = P/k + P/k^2 + ... + P/k^n

(1/k) = t

S = Pt + Pt^2 + Pt^3 + ... + Pt^n

S * t = Pt^2 + Pt^3 + Pt^4 + ... + Pt^(n + 1)

St - S = Pt^(n + 1) - Pt

S * (t - 1) = P * t * (t^(n) - 1)

S = P * t * (t^(n) - 1) / (t - 1)

S = P * (1/k) * ((1/k)^n - 1) / (1/k - 1)

S = P * (1/k) * (k^(-n) - 1) / ((1 - k) / k)

S = P * (k^(-n) - 1) / (1 - k)

S = P * ((1 + i/12)^(-n) - 1) / (1 - (1 + i/12))

S = P * ((1 + i/12)^(-n) - 1) / (1 - 1 - i/12)

S = P * (1 - (1 + i/12)^(-n)) / (i/12)

S = P * 12 * (1 - (1 + i/12)^(-n)) / i

L = P/k + P/k^2 + P/k^3 + ... + P/k^n + R/k^n

L = S + R/k^n

L = 12 * P * (1 - (1 + i/12)^(-n)) / i + R/(1 + i/12)^n

L = (12/i) * P * (1 - (1 + i/12)^(-n)) + R * (1 + i/12)^(-n)

Still looks like hell, but we're there. I promise you. Let's suppose that after 360 payments (a 30-year loan), your remaining balance is 0. You borrowed $100,000 at 6%. What would your payments be?

100,000 = L

0 = R

6% = 6/100 = 0.06 = i

360 = n

L = (12/i) * P * (1 - (1 + i/12)^(-n)) + R * (1 + i/12)^(-n)

100000 = (12/0.06) * P * (1 - (1 + 0.06/12)^(-360)) + 0 * (1 + 0.06/12)^(-360)

100000 = (1200/6) * P * (1 - (1 + 6/1200)^(-360)) + 0

100000 = 200 * P * (1 - (1 + 1/200)^(-360))

1000 * 100 = 200 * P * (1 - (201/200)^(-360))

5 * 100 = P * (1 - (200/201)^360)

500 / (1 - (200/201)^360) = P

P = 599.55052515275239459146124368448

Your monthly payment would be $599.55 (they'd probably round that up to a nice even $600 and your final payment would be about $400 or so).

That's just principal and interest, mind you, but that's how they calculate it.

The rule of thumb is $50 for every $10,000 of a 30-year mortgage, but that comes out with a payment a bit higher than what it would be right now because the interest rates are so low, like a 30-year fixed right now on $100,000 at a present mortgage rate of 3.9% comes out to a principle and interest payment of $473, while the rule of thumb says it would be $500. Of course, that doesn't include the primary mortgage insurance (PMI) you have to pay for should you put less than 20% down, which can add as much as a $100 a month to that $100,000 mortgage.

Another thing you can do is half the mortgage amount, multiply it by the interest rate, multiply the resulting amount by the number of years your mortgage is for, add that amount to the original mortgage amount, and then divide that total by the number of months in the number of years your mortgage is for. The actual amount will come out a little higher because of daily rather than annual compounding, but it'll also get you in the ballpark.

If you want to be right on the money, though, just Google "mortgage calculator" and use an online mortgage calculator to figure it.

Online: Look up "Mortgage Calculator"

In Excel: =PMT (rate, nper, pv, [fv], [type])

Ask your real estate agent. After you build good credit and are over 25.

You google mortgage payment calculator