Maths formula for calculating mortgage repayments

thebourke

I am looking for the mathematical formula to calculate the mortgage repayments
for a 100,00euro mortgage at 4% APR.Would anyone have this formula?

Yakuza

The annual payment would be given by €[latex]\frac{100000}{\frac{1-1.04^{-20}}{.04}} [/latex], or €7358.17 (this assumes you pay at the end of the year)

The monthly payment is not quite the above over 12, as you are paying off the mortgage faster by paying monthly:

Turn 4% into a monthly rate (1.04^(1/12)-1), or 0.00327374).

Using the above as a template (and working in months), you get: €[latex]\frac{100000}{\frac{1-1.0.00327374^{-240}}{0.00327374}} [/latex], or €602.22 (again, assuming you pay at the end of the month).

The interest rate that banks quote normally isn't the APR (but you will find it on the blurb), that's the one you should plug into the above formulae.

Edit : Note I assumed a term of 20 years for the purposes of the above calcs.

Tom.D.BJJ

Alternatively, you could use excel

=-PMT(0.04/12,300,100000)

300 is based on 25 years at 12 payments per year, so if it's 30 years change that to 360, or alternatively 240 for 20 years.

Yakuza

I'm nit-picking here, but 0.04/12 is not the same monthly interest rate as an APR of 4%. It's close, but not the same. A monthly rate of 0.04/12 yields an APR of 4.074% ---> [1+(.04/12)]^12 -1.

Using excel, =-PMT(0.04,20,100000) and =-PMT(0.00327374,240,100000) give the same figures as I quote above. I just show the actual formula