This mortgage calculator can be used to find the monthly repayment for an amortizing loan, as well as the term, rate, down payment and principal (loan amount).
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The calculations are based on this formula: \begin{equation*} M = (L-D) \times \frac{i \times (1+i)^n}{(1+i)^n - 1}. \end{equation*}
Where \begin{align*} M &= \text{Monthly repayment,} \\ L &= \text{Loan amount (or principal),} \\ D &= \text{Down payment,} \\ i &= \frac{\text{Interest rate}}{\text{Number of compounding periods per year}} \end{align*} and \begin{align*} n &= \text{Total number of compounding periods.} \end{align*}
As an example, to find the monthly repayment for a $250,000 loan at 7.5% over 25 years, you would do the following: \begin{align*} L &= 250,000 \\ D &= 0 \\ i &= 0.075 \div 12 = 0.00625 \qquad \text{(Compounded twelve times a year)} \\ n &= 25 \times 12 \end{align*} Then: \begin{align*} M &= (250,000 - 0) \times \frac{0.00625 \times (1 + 0.00625)^{300}}{(1 + 0.00625)^{300} - 1} \\ M &= 1847.48 \end{align*}