Language:

All principal payments are equal in amortizing loans, meaning that the amount of your payment that goes towards your principal balance is the same every time. But the size of the payments decreases over time. This is due to the interest payments becoming smaller as the remaining loan balance decreases, meaning the total installments also shrink.

Between fixed-rate mortgages and amortizing loans, amortizing loans are cheaper, but they are also less common.

The reason why most people still choose fixed-rate mortgages over amortizing loans is that you’re often permitted to borrow more money with fixed-rate mortgages, and the installments generally aren’t as high in the beginning. This could, for instance, enable you to buy a bigger home, even though you would pay more interest in the long run.

Formula

$$\begin{array}{cc}\text{Principalpayment}& \\ =& \\ \frac{\text{loanamount}}{\text{numberofinstallments}}& \end{array}$$

$$\text{Principalpayment}=\frac{\text{loanamount}}{\text{numberofinstallments}}$$ |

Formula

$$\begin{array}{cc}\text{Interest}& \\ =& \\ \text{remainingloan}\cdot \text{interestrate}& \end{array}$$

$$\text{Interest}=\text{remainingloan}\cdot \text{interestrate}$$ |

Formula

$$\begin{array}{cc}\text{Installment}& \\ =& \\ \text{principalpayment}+\text{interest}& \end{array}$$

$$\text{Installment}=\text{principalpayment}+\text{interest}$$ |

Formula

$$\begin{array}{cc}\text{Remainingloan}& \\ =& \\ \text{previousremainingloan}& \\ -& \\ \text{principalpayment}& \end{array}$$

$$\begin{array}{llll}\hfill \text{Remainingloan}& =\text{previousremainingloan}\phantom{\rule{2em}{0ex}}& \hfill & \phantom{\rule{2em}{0ex}}\\ \hfill & \phantom{\rule{2em}{0ex}}-\text{principalpayment}\phantom{\rule{2em}{0ex}}& \hfill & \phantom{\rule{2em}{0ex}}\end{array}$$

Example 1

Ben and Jerry want to buy an apartment in London. They consider taking out an amortizing loan. They’ve made a budget and determined that they’re able to pay an annual installment of no more than £$205\phantom{\rule{0.17em}{0ex}}000$. They want to borrow £$1\phantom{\rule{0.17em}{0ex}}500\phantom{\rule{0.17em}{0ex}}000$ with an annual interest rate of $3.5$ %, with a ten-year repayment period. What will be the first installment on this loan? Can they afford it?

The first installment amounts to £$202\phantom{\rule{0.17em}{0ex}}500$, which is below the limit Ben and Jerry set for themselves. They can afford the amortizing loan.