Annuity of a loan for a given capital, duration and interest rate formula
Description of the Annuity of a loan for a given capital, duration and interest rate formula
This formula permits the calculation of the annuity to pay for the reimbursement of a loan with an amount \( C \), an interest rate \( r \) and a duration of \( N \) periods. It allows us to answer for example the following question: How much does it cost me every month if I want to lend the amount \( C \) at an interest rate \( r \), over a duration of \( N \) months.
Formula
\[ m=\frac{C\cdot\frac{r}{n}}{1-(1+\frac{r}{n})^{-N}} \ \]
Symbols
\(C\ \)
Start capital
\(m\ \)
Annuity
\(n\ \)
Number of payments per year
\(N\ \)
Total number of annuities (number of years times number of payments per year)
\(r\ \)
Nominal annual interest rate