Mortgage Calculator

Step-by-step solution

1. 1

   Identify the inputs

   A mortgage spreads the loan over equal monthly payments — the formula below gives the exact payment.

   $$M = P \cdot \frac{i \cdot (1+i)^{N}}{(1+i)^{N} - 1}$$

   • P = 400000 - 80000 = 320000
   • r = 6.5%
   • t = 30
   • n = 12
   • N = 360
2. 2

   Compute the monthly rate

   The annual rate becomes a monthly rate: i = 13/2400 as an exact fraction.

   $$i = \frac{r}{12} = \frac{\frac{13}{2}}{12} = \frac{13}{2400}$$
3. 3

   Apply the payment formula

   The fixed monthly payment is 2,022.62.

   $$M = 320000 \cdot \frac{\frac{13}{2400} \cdot \left(\frac{2413}{2400}\right)^{360}}{\left(\frac{2413}{2400}\right)^{360} - 1} \approx 2{,}022.62$$
4. 4

   Total cost of the loan

   Over the full term you pay 728,142.36, of which 408,142.36 is interest.

   $$\text{total} = M \cdot N = 2{,}022.62 \cdot 360 = 728{,}142.36$$
5. 5

   The amortization schedule

   Each year the interest share shrinks while the principal share grows — the table and curves show the 30-year amortization.