The most common method for calculating the loan payments is the fixed-rate fully amortizing loan. This type of loan involves regular, equal payments that cover both interest and principal over life of the loan.
The key concepts and formulas:
The key concepts and formulas:
- Loan Amount (\(P\)) - this is the initial amount of money that is borrowed.
- Interest rate (Annual Percentage Rate, \(r\)): The annual cost of borrowing, expressed as a percentage. For monthly payments, the monthly interest rate is \(\frac{r}{12}\).
- Loan Term \(n\) - the duration of the loan, typically expressed in years. For monthly payments, the total number of payments is \(n\cdot 12\).
- Monthly Payment (PMT) - the formula to calculate the monthly payment for a fixed-rate loan can be written as:
\begin{equation}
PMT = P \cdot \frac{r(1+r)^n}{(1+r)^n -1}
\end{equation}
where:
- \(P\) is the principal loan amount.
- \(r\) is the monthly interest rate (annual divided by 12)
- \(n\) is the total number of payments (loan term in years multiplied by 12).
Example 1 - if the principal loan amount is 10000 Euros, calculate the monthly payment if the monthly interest rate is 2, and the duration of the loan is 60 years.
\begin{equation}
P = 10000, r = 2/100 = 0.02/12 = 0.0016666666666666668, n = 60*12 = 720
\end{equation}
\begin{eqnarray}
PMT &=& P \cdot \frac{r(1+r)^n}{(1+r)^n -1}\\
PMT &=& 1000\cdot \frac{0.0016666666666666668(1+0.0016666666666666668)^{720}}{(1+0.0016666666666666668)^{720} - 1}\\
PMT &=& 23.86
\end{eqnarray}
The person will have to pay 23.86 Euros every month for 60 years to payoff the debt.
Example 2 - If the principal loan amount is 100000 Euros, calculate the monthly payment if the monthly interest is 10\%, and the duration of the loan is 10 years.
\begin{equation}
P = 100000, r = 10/100 = 10/12 = 0.008333333333333333, n = 10*12 = 120
\end{equation}
\begin{eqnarray}
PMT &=& P \cdot \frac{r(1+r)^n}{(1+r)^n -1}\\
PMT &=& 100000\cdot \frac{0.008333333333333333(1+0.008333333333333333)^{120}}{(1+0.008333333333333333)^{120} - 1}\\
PMT &=& 1321.51
\end{eqnarray}
The person will have to pay 1321.51 Euros every month for 10 years to payoff the debt.