You take out a long-term mortgage loan, which means you are tied to a debt for 30 years. Taking on a debt is an important decision because it involves a large amount. We often quickly agree to it, without having thought about the consequences of a mortgage. Because the interest deduction before taxes has been adjusted, the repayment method should be considered for new mortgages. To benefit from it, you have two options for repayment, namely the linear and annuity method. How do you calculate the mortgage repayment and how much have you repaid after so many years?
Mortgage repayment
- Mortgage choice
- How does the linear method work?
- How does the annuity method work?
- How much mortgage repayment?
- What can we do with this?
Mortgage choice
When taking out a mortgage, you have the option to choose between repayment options during the term and afterwards. Because the mortgage interest deduction has been reformed, the primary choice will be between the linear and annuity repayment method. This is because interest deduction is still possible. The question is how much you actually work on repayment with these methods. We know that the straight-line repayment method is conservative and it has a beneficial effect on repayment. Nevertheless, the annuity mortgage may be preferred, because the costs are always at the same level. How does the rate of repayment compare between the annuity and linear method to achieve 100% repayment after 30 years?
How does the linear method work?
When repaying using the linear method, you repay the same part per month regardless of the interest rate. Normally the term is 30 years, which means we have to pay 1/30th of the repayment every year. The repayment is therefore linear, with the advantage that the amount of the interest payment also decreases linearly over the years. To obtain this type of mortgage, it is necessary to have sufficient capacity for the first year, because then the costs are relatively high.
How does the annuity method work?
With this method, the same amount is spent on expenses every year, but the interest and repayment share changes within that amount. The following relationship can be indicated for this purpose, for example 4% interest applies:
- first year repayment = 100% * 0.04 / [1-1.04^(-30)] – 100% * 0.04 = 1.78%;
- second year repayment = 100% * 0.04 / [1-1.04^(-30)] – (100%-1.78%) * 0.04 = 1.85%;
- thirtieth year repayment = 100% * 0.04 / [1-1.04^(-30)] – (100%-94.44%) * 0.04 = 5.56%.
The most convenient way to determine this is using Excel, so that the interest share and repayment can be determined quickly and easily per year. Always check that the total repayment amounts to 100% of the mortgage debt. This allows you to quickly gain insight into how much you can repay over time using the annuity method.
How much mortgage repayment?
It is clear that if you have just started repaying for a few years, you will be around 0% repayment. Normally you have to repay it in 30 years, which means that every method ends in 100% repayment after the term. But how often does it happen that we have to terminate the mortgage loan prematurely. Then it is certainly interesting to know how much you have actually repaid in the event of an interim repayment. Below is the table comparing an interest rate of 3%, 4% and 5% on the annuity mortgage with the linear mortgage. Please note that the repayment amount is also expressed in percentages to obtain a clear comparison to ultimately repay 100%.
YearMethod |
Annu.3% |
Annu.4% |
Annu.5% |
Linear |
5 years |
11% |
10% |
8% |
17% |
10 years |
24% |
21% |
19% |
33% |
15 years |
39% |
36% |
32% |
50% |
20 years |
56% |
53% |
50% |
67% |
25 years |
77% |
74% |
72% |
83% |
What can we do with this?
As soon as the interest rate is known, we know what percentage is actually repaid with the annuity method. The lower the interest rate, the sooner the repayment process will be relatively accelerated. In other words, when interest rates are high, the relative repayment is slower. As the numbers show, the fastest way to pay off is using the linear method. This has to do with the fact that this type of mortgage is not linked to the interest rate for repayment. Anyone who wants certainty about accelerated repayment or accelerated build-up of equity chooses the linear mortgage. However, if one wants to borrow as much as possible within the financial scope, the annuity mortgage will be chosen. The costs are spread over the years, but are unchanged. This is a good starting point for financing a mortgage, but the rate of repayment in the first years lags far behind the linear method. If half of the debt is already repaid after 15 years with the linear method, this will only be achieved after 20 years with the annuity method.
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