# How can you calculate penalty interest if mortgage changes

If a mortgage prematurely is changed before the end of term then it is a breach of contract. The old mortgage lender has right on interest compensation till the end of the ongoing contract. Before you really will change your mortgage it is important to know how much you will need to pay for this. How is the penalty interest calculated with the linear and annuity mortgage?

## Why is it imposed?

The height of the penalty is determined by the overall value of the still expected contractual interest returns. As this contract will prematurely will be ended it is considered a breach of contract. This means that the mortgage lender still has right on compensation over the due months or years. The longer this contract still has to go the higher the penalty will be. If possible this penalty can be financed within the new mortgage so that you have no direct financial problems from it. How is this calculated and how is the present value method used within that?

## Present value method

What you have to pay for interest costs doesn't match what you have to pay for it now. Over the future term you still can get interest which can be deducted on the penalty interest. This is done by the present value method using the following formula:

• Pv = present value = Fv / (1+i)t within it;
• Fv = future value;
• i = interest rate per year;
• t = time in years.

If you have determined how much interest you would have paid in the future according to contract, then you need to correct it with this factor. In that way the present value over the future interest payments can be determined.

## How to calculate it?

You have a mortgage for 165,000 dollar and you planned to pay it off in 30 years. Your present mortgage contract is for 10 years at an interest rate of 4.5%. You are considering changing the running contract prematurely after 8 years so you can profit from a very low interest rate. From the beginning of the 9-th year you want to have arranged it. How much penalty interest do you need to pay?

## Linear mortgage

With a linear mortgage you pay off the same amount every month so that the interest also drops accordingly. Every year you will pay off 165,000/30 = 5,500 dollar so that the debt and interest costs lower. It means the following:

• Start 9-th year debt = 165,000 – 8 * 5,500 = 121,000 dollar;
• Start 10-th year debt = 165,000 – 9 * 5,500 = 115,500 dollar;
• End 10-th year debt = 165,000 – 10 * 5,500 = 110,000 dollar.

Over these 2 years you still would have paid (121,000+115,500) / 2 * 0.045 + (115,500 + 110,000) / 2 * 0.045 = 5,321.25 + 5,073.75 = 10,395 dollar on interest. Corrected with the present value method this means that at this moment you have to compensate 5,321.25/(1+0.045)^1 + 5,073.75/(1+0.045)^2 = 5,092.11 + 4,646.19 = 9,738.30 dollar.

## Annuity mortgage

With the annuity mortgage you pay every year the same amount consisting interest and payoff. The ratios between these change every year so that every needs to be calculated how high the interest and payoff portion is. Costs are calculated as follows:

• Costs per year = S * i / [1 – (1+i)-n] within it;
• S = initial mortgage debt;
• i = interest rate per year;
• n = number of years for payoff;
• S = 165,000 * 0.045 / [1 – 1.045-30] = 10,129.60 dollar per year;
• a = payoff 1-st year = 10,129.60 – 165,000 * 0.045 = 2,704.60 dollar.

The amount for payoff will grow every year gradually, but within the calculation of future interest portions the payoff 1-st year is essential. How much interest will you need to pay from beginning 9-th till end of 10-th year?:

• Payoff sum = a*[(1+r)n-1]/(r);
• Payoff 9-th year = 2,704.60 * {[1.0459-1] – [1.0458-1] } / 0.045 = 3,846.21 dollar;
• Interest portion 9-th year = 10,129.60 – 3,846.21 = 6,283.39 dollar;
• Payoff 10-th year = 2,704.60 * {[1.04510-1] – [1.0459-1]} / 0.045 = 4,019.30 dollar;
• Interest portion 10-th year = 10,129.60 – 4,019.30 = 6,110.30 dollar.

This needs to be corrected with the present value method:

6,283.39/(1+0.045)1 + 6,110.30/(1+0.045)2 = 6,012.82 + 5,595.38 = 11,608.20 dollar.

## Changing or not

When is it wise to change your running contract? If the contract almost comes to an end then it is logical that you change it. Often you use the same mortgage lender or you search for a cheaper one. If you change it prematurely then it is breach of contract. The penalty interest can be a lot of money for sure. In previous example it is 6-7% of the initial mortgage. This for sure is a big portion and needs to be financed within a new mortgage. It is advisable to wait in such cases so that the penalty will get lower. Next to that it depends also on how much you can gain when choosing a cheaper mortgage. It is always necessary to calculate how much it is. In some countries this penalty can be deducted from taxes and can give some compensation in the costs.

Previous calculation is based on an interest rate per year. Normally it will be calculated per month as it is more accurate. If you want to have an exact calculation go to a certified mortgage specialist or contact your bank.

Source: http://financieel.infonu.nl/hypotheek/138899-boeterente-berekening-hoe-reken-je-de-boeterente-uit.html

http://nl.wikipedia.org/wiki/Contante_waarde

http://en.wikipedia.org/wiki/Present_value