How do you calculate the annuity mortgage

To buy a house most people will need to get a loan or mortgage at a bank. One type of loan is the annuity mortgage which in some countries can be used for interest tax refund. If you want to buy a house you will need to know how much it will cost per month and during contract term. How do you calculate yourself how much the annuity mortgage costs and what aspects do you have to consider with that?


What is the annuity method?

If you want to get a mortgage profiting of tax refund (if in your country applicable) you will need to have a mortgage based on the annuity method. But what is that, the annuity and how you can calculate it easily? With the annuity the monthly costs are calculated based on a mortgage debt and a certain interest rate. What you pay per month doesn't change but the ratio between costs for interest and payoff change with time. At first you pay a lot of interest and a small part payoff, but this ratio changes. In time payoff grows and interest drops. How do you calculate this?


Theory behind it

The annuity determines the total costs per month and is based on interest. How much you pay depends on the height of your debt and interest rate. Use the following formula:

  • Cost per month = d * i/month / (1 - (1 + i/month)-n) with in it:
  • d = debt of the loan aka mortgage;
  • i/month = interest rate per month = (1 + i/year)1/12 -1;
  • n = number of months you will need to pay off your mortgage. Normally this is 30 years and that is 360 months.

Based on previous formula you van quickly determine how much costs you per month have when closing a certain mortgage.


Calculation example

You want to buy a house for which you need to have a mortgage of 146.500 dollar. On the internet you see different interest rates with different mortgage providers. You can get a mortgage for a minimal term of 10, 15, 20, 25 or 30 years. In this case assume that the current interest rate is 4.65%. How much do you have to pay per month?:

  • Interest per month = (1 + 0.0465)1/12 – 1 = 0.003795 = 0.3795%;
  • Costs per month = 146,500 * 0.003975 / (1 – 1.003975-360) = 765.98 dollar.


Of course this amount is composed out of interest with payoff. This means also you cannot deduct this amount from tax, so what is the interest part you can deduct?


How much interest do you pay?

If in your country you can deduct interest from tax you will need to know how much interest you pay monthly. How do you calculate the interest rate you can deduct from tax?:

  • In the first month you pay 146,500 * 0.003975 = 582.34 dollar for interest;
  • You will pay off 765.98 – 582.34 = 183.64 dollar;
  • Your debt in the second month will be 146,500 – 183.64 = 146,316.36 dollar.
  • As you pay the second month again 765,98 dollar the following happens:
  • Interest 2-nd month = 146,316.36 * 0.003975 = 581.61 dollar;
  • Payoff 2-nd month = 765.98 – 581.61 = 184.37 dollar.

You see that the interest portion drops and the payoff grows. You can use Excel to calculate this further. You will see that the interest portion practically will be zero dollars in the last month and that payoff is great. In thirty year you will have:

  • Total costs: 360 * 765.95 = 275,745.60 dollar;
  • Total payoff = 146,500 dollar;
  • Total interest costs = 275,745.60 – 146,500 = 129,245.60 dollar.