This mortgage points calculator helps you estimate and compare your monthly payment in case of a loan without points versus one with prepaid interest points. There is in depth information on this topic below the tool.
How does this mortgage points calculator work?
This is a handy personal finance calculator that can help you when trying to figure out whether a mortgage with discount points is preferable instead of a normal one without prepaid interest points. The variables that should be provided to simulate such scenario are:

Mortgage amount (Ma) represents how much you intent to borrow.

No points  Annual interest rate (r) refers to yearly interest you would pay in case of a simple mortgage.

Loan term (Lt) that can be either in years or months.

With points  Annual interest rate (rp) represents the rate of interest discounted you would pay in case you choose to make an upfront payment. Please note, that in practice lenders offer for each point purchased a lower interest rate diminished with 1/8% (0.125%).

Number of points paid (Pp). Please note that usually 1 point is equivalent to 1% from the loan amount taken. For instance 1 point from a mortgage of $200,000 is equal to $2,000.
The algorithm behind this mortgage points calculator is based on the following formulas:
Compare mortgage payments 
Without points 
With points 
(A) Monthly payment value 
A1 
A2 
(B) Total paid for the mortgage 
B1 
B2 
(C) Total interest paid 
C1 
C2 
(D) Upfront cost with points 
 
D2 
(E) Savings from interest per month 
 
E2 
(F) No. of months to get back upfront cost with points from interest being saved 
 
F2 
(G) Total savings from interest 
 
G2 
B1 = A1 * N
B2 = A2 * N
C1 = B1 – Ma
C2 = B2 – Ma
D2 = Ma * Pp/100
E2 = (C1 – C2)/N
F2 = Round(D2/E2,0)
G2 = C1 – C2
Understanding the role of points in a mortgage
In financial industry, more specifically in mortgage contracts points represent a form of prepaid interest having a double role:

From borrower’s perspective it is a way to take money through a loan at a lower interest rate by making an upfront payment to pay such points. This is usually considered as a onetime cost associated with the transaction. Buying interest points will result in a smaller monthly payment than in case of a standard mortgage. It also should be mentioned that there are cases in which people take mortgage points in order to qualify for a certain loan.

From lender’s point of view the discounted points represent a way to increase its yield on the loan, which in such case consists the earnings from the negotiated interest rate the borrower has to pay plus the upfront payment the lender receives at the beginning of the contract.
Example of a calculation
Let’s simulate a scenario with a standard mortgage offering a fixed rate of 5% over 30 years, versus a one taken with 3 points paid offering an interest rate of 4.625, while the amount borrowed is $100,000:
Compare mortgage payments  Without points  With points 

Monthly payment value  $536.82  $514.14 
Total paid for the mortgage  $193,255.78  $185,090.23 
Total interest paid  $93,255.78  $85,090.23 
Upfront cost with points    $3,000.00 
Savings from interest per month    $22.68 
No. of months to get back upfront cost with points from interest being saved    133 
Total savings from interest    $8,165.56 