Add equated_monthly_installments.py in Financials (#5775)

* Add equated_monthly_installments.py in Financials

* Formatting

* More formatting, Descriptive names

* Errors with name change

* Formatting

* Formatting, Naming Error

* dedent

* Update DIRECTORY.md

Author: Rohanrbharadwaj

DIRECTORY.md

@@ -298,6 +298,7 @@
 
 ## Financial
   * [Interest](https://github.com/TheAlgorithms/Python/blob/master/financial/interest.py)
+  * [EMI Calculation](https://github.com/TheAlgorithms/Python/blob/master/financial/equated_monthly_installments.py)
 
 ## Fractals
   * [Julia Sets](https://github.com/TheAlgorithms/Python/blob/master/fractals/julia_sets.py)

financial/equated_monthly_installments.py

@@ -0,0 +1,61 @@
+"""
+Program to calculate the amortization amount per month, given
+- Principal borrowed
+- Rate of interest per annum
+- Years to repay the loan
+
+Wikipedia Reference: https://en.wikipedia.org/wiki/Equated_monthly_installment
+"""
+
+
+def equated_monthly_installments(
+    principal: float, rate_per_annum: float, years_to_repay: int
+) -> float:
+    """
+    Formula for amortization amount per month:
+    A = p * r * (1 + r)^n / ((1 + r)^n - 1)
+    where p is the principal, r is the rate of interest per month
+    and n is the number of payments
+
+    >>> equated_monthly_installments(25000, 0.12, 3)
+    830.3577453212793
+    >>> equated_monthly_installments(25000, 0.12, 10)
+    358.67737100646826
+    >>> equated_monthly_installments(0, 0.12, 3)
+    Traceback (most recent call last):
+        ...
+    Exception: Principal borrowed must be > 0
+    >>> equated_monthly_installments(25000, -1, 3)
+    Traceback (most recent call last):
+        ...
+    Exception: Rate of interest must be >= 0
+    >>> equated_monthly_installments(25000, 0.12, 0)
+    Traceback (most recent call last):
+        ...
+    Exception: Years to repay must be an integer > 0
+    """
+    if principal <= 0:
+        raise Exception("Principal borrowed must be > 0")
+    if rate_per_annum < 0:
+        raise Exception("Rate of interest must be >= 0")
+    if years_to_repay <= 0 or not isinstance(years_to_repay, int):
+        raise Exception("Years to repay must be an integer > 0")
+
+    # Yearly rate is divided by 12 to get monthly rate
+    rate_per_month = rate_per_annum / 12
+
+    # Years to repay is multiplied by 12 to get number of payments as payment is monthly
+    number_of_payments = years_to_repay * 12
+
+    return (
+        principal
+        * rate_per_month
+        * (1 + rate_per_month) ** number_of_payments
+        / ((1 + rate_per_month) ** number_of_payments - 1)
+    )
+
+
+if __name__ == "__main__":
+    import doctest
+
+    doctest.testmod()