# Calculate how much loan mortgage interest you need to pay

If you have a mortgage or you want to buy a house, you will need to know how much interest you need to pay. You want to know how much the costs are per year and month but also what it costs during contract term. How can you calculate interest costs based on the linear or annuity mortgage?

If you are interested in buying a house you surely need to know how much it will cost. Most essential question with that is which type of mortgage you want to use and if it gives you some tax benefits (if possible in your country). Sometimes these benefits can be a substantial amount. How much your loan will cost is determined by the method of paying off the mortgage as well as the interest rate. How much interest do you actually have to pay during contract term?

## Mortgage deductible

In some countries interest costs for the mortgage are deductible for taxes. Think about the Nederlands where house owners get back 42% aka 52% of the interest costs if they have an income till scale 3 aka 4. From 2014 this will be gradually reduced in 28 years from 52% till 38% (lowering steps 0.5% per year). The deductibility ensures house owners the reduction of debts. The deductibility is only applied for loans which are paid off through the linear or annuity mortgage. How do you calculate the interest costs?

## Linear

Linear payoff means that the debt also reduces linear. This also means that the interest cost also reduce in a linear way. What if you have a mortgage of 215,000 dollar with 3.9% for interest, how much does it cost you?:

• Payoff per year = 215,000 / 30 = 7,166.67 dollar per year;
• Total interest costs = (215,000 + 7,166.67) / 2 * 0.039 * 30 = 129,967.50 dollar;
• Total refund from tax = 129,967.50 * 0.42 = 54,586.35 dollar;
• Correction interest costs = 129,967.50 – 54,586.35 = 75,381.15 dollar.

But what if you like to know how much you pay for interest in a specific year in the future, how do you do that? You like to know how much interest it costs in the 12-th year, how do you do that?:

• Mortgage debt start 12-th year = 215,000 – 7,166.67 * 11 = 136,166.63 dollar;
• Mortgage debt end 12-th year = 215,000 – 7,166.67 * 12 = 128,999.96 dollar;
• Interest cost 12-th year = (136,166.63 + 128,999.96) / 2 * 0.039 = 5,170.75 dollar.

If you can deduct it from taxes you will get back 5,170.75 * 0.42 = 2,171.72 dollar.

## Annuity

Another payoff method is the annuity. Every year you will pay the same as it covers interest and payoff in one amount. At first the interest costs are high and payoff is relative low and those changes with time in low interest costs and high payoff. How much interest costs do you have with this?

• Costs per year = 215,000 * 0.039 / (1 – 1.039-30) = 12,282.95 dollar per year;
• Total costs = 12,282.95 * 30 = 368,488.50 dollar;
• Total interest costs = 368,488.50 – 215,000 = 153,488.50 dollar;
• Total refund from tax = 153,488.50 * 0.42 = 64,465.17 dollar;
• Correction interest costs = 153,488.50 – 64,465.17 = 89,023.33 dollar.

This already shows that the annuity method for payoff is relatively more expensive with respect to the linear method. What if you want to calculate the interest costs in the 12-th year, how do you do that with the annuity method?:

• Payoff in 1-st year = 12,282.95 – 215,000 * 0.039 = 3,897.95 dollar;
• Payoff in 12-th year = 3,897.95 / 0.039 * [(1.03912 – 1) – (1.03911 – 1)] = 5,937.55 dollar;
• Interest costs in 12-th year = 12,282.95 – 5,937.55 = 6,345.40 dollar.

If you have deductibility you can get back 6,345.40 * 0.42 = 2,665.07 dollar in the 12-th year.

Using previous methods you can exactly calculate how much interest costs you have for a specific year. If you want to buy a house always get advice from a certified mortgage specialist so that you will know what your interest costs will be.

Source: http://financieel.infonu.nl/hypotheek/139229-bereken-hoeveel-rente-u-aan-de-hypotheek-kwijt-bent.html

http://www.rijksoverheid.nl/onderwerpen/koopwoning/vraag-en-antwoord/wat-is-de-hypotheekrenteaftrek.html

http://www.wiskundebijles.nl/wiskunde/financieelrekenen/annuiteit/annuiteit.htm

http://nl.wikipedia.org/wiki/Annu%C3%AFteit