### Calculating the car loan payments

Let’s say that you want to purchase a car for \$15000. You only have \$5000. A bank offers you \$10000 at 7% interest which you have to pay back in 5 years. What is your yearly payment for the car?

Here is what we know

• Car price \$15000
• Loan amount \$10000
• Interest rates 7% per year
• Duration 5 years
• Payments ? - We need to solve for this.

Before we build our loan amortization table we need to calculate the yearly payment for our car loan. To calculate this we need the `numpy` module/package.

Lets load our modules.

``````import pandas as pd
import numpy as np``````

Next we setup the variable that are known and calculate car payments.

``````car_loan = 10000
interest = 0.07
years = 5
car_payments = np.pmt(rate = interest, nper = years, pv = -car_loan)
print(car_payments)``````
``## 2438.9069444137394``

Our car loan will cost us \$2438 in yearly payments. We can build a payment schedule table and see how our loan balance will go down to zero at the end of the fifth year. First we will show you the entire code and then walk you through each step.

``````car_loan = 10000
interest = 0.07
years = 5
car_payments = np.pmt(rate = interest, nper = years, pv = -car_loan)
loan_table = np.zeros((5,6))
loan_table = pd.DataFrame(loan_table)
loan_table.columns = ["Year", 'Initial_Balance', "Payments", "Interest",
"Principal", "Ending_Balance"]
loan_table.iloc[0,0] = 1
loan_table.iloc[0,1] = car_loan
loan_table.iloc[0,2] = car_payments
loan_table.iloc[0,3] = car_loan * interest
loan_table.iloc[0,4] = car_payments - (car_loan * interest)
loan_table.iloc[0,5] = car_loan - (car_payments - (car_loan * interest))
for i in range(1,5):
loan_table.iloc[i,0] = i + 1
loan_table.iloc[i,1] = loan_table.iloc[(i-1), 5]
loan_table.iloc[i,2] = car_payments
loan_table.iloc[i,3] = loan_table.iloc[i,1] * interest
loan_table.iloc[i,4] = car_payments - (loan_table.iloc[i,1] * interest)
loan_table.iloc[i,5] = loan_table.iloc[i,1] - (car_payments - (loan_table.iloc[i,1] * interest))

loan_table = loan_table.round(2)

with pd.option_context("display.max_rows",None,"display.max_columns", None):
print(loan_table)``````
``````##    Year  Initial_Balance  Payments  Interest  Principal  Ending_Balance
## 0   1.0         10000.00   2438.91    700.00    1738.91         8261.09
## 1   2.0          8261.09   2438.91    578.28    1860.63         6400.46
## 2   3.0          6400.46   2438.91    448.03    1990.87         4409.59
## 3   4.0          4409.59   2438.91    308.67    2130.24         2279.35
## 4   5.0          2279.35   2438.91    159.55    2279.35            0.00``````

As you can see our final balance at the end of year 5 is 0. Lets go through this code.

First we calculate the car_payments for each year.

``````car_loan = 10000
interest = 0.07
years = 5
# We use the np.pmt() function to calculate the payments
car_payments = np.pmt(rate = interest, nper = years, pv = -car_loan)``````

Next we create an empty data frame to hold our yearly values. We will fill this table using a for loop.

``````# This creats a table of 5 rows and 6 columns filled with zeros
loan_table = np.zeros((5,6))
# Convert it to a dataframe
loan_table = pd.DataFrame(loan_table)
# We change the column names to relevant fields
loan_table.columns = ["Year", 'Initial_Balance', "Payments", "Interest",
"Principal", "Ending_Balance"]
print(loan_table)``````
``````##    Year  Initial_Balance       ...        Principal  Ending_Balance
## 0   0.0              0.0       ...              0.0             0.0
## 1   0.0              0.0       ...              0.0             0.0
## 2   0.0              0.0       ...              0.0             0.0
## 3   0.0              0.0       ...              0.0             0.0
## 4   0.0              0.0       ...              0.0             0.0
##
## [5 rows x 6 columns]``````

Now that we have out empty table we need to fill the table with our calculations. We need to calculate the first column manually and then we can fill the rest using a for loop using the first values. This is similar to excel, where we need to calculate the first row manually and then drag down to copy the formula to fill the remaining columns.

One thing to note about Python versus R is that Python indexing starts at 0 and R starts at 1. So our column 1 and row 1 in R is column 0 and row 0 in Python. So we modify that code accordingly.

``````# Row 0 and column 0 is our Year 1.
# use iloc[] to loacate that
loan_table.iloc[0,0] = 1
# Initial balance it the car_loan amount
loan_table.iloc[0,1] = car_loan
# car payments are the same we calculated above
loan_table.iloc[0,2] = car_payments
# interest payment is initial balance * interest
loan_table.iloc[0,3] = car_loan * interest
# Priciple is car payment - interest
loan_table.iloc[0,4] = car_payments - (car_loan * interest)
# Ending balance is intial balance - principle
loan_table.iloc[0,5] = car_loan - (car_payments - (car_loan * interest))``````

Once we have the first row filled we can now run the for loop to calculate all the other values.

``````# Our loop will run from row 1 to 4
for i in range(1,5):
# First row is the year
loan_table.iloc[i,0] = i + 1

# The initial balance is previous years ending balance
loan_table.iloc[i,1] = loan_table.iloc[(i-1), 5]

# The payments are the car payments
loan_table.iloc[i,2] = car_payments

# Interest each year is initial balance * interest rate
loan_table.iloc[i,3] = loan_table.iloc[i,1] * interest

# Principle amount is payment - interest amount
loan_table.iloc[i,4] = car_payments - (loan_table.iloc[i,1] * interest)

# Ending balance is initial balance - principle
loan_table.iloc[i,5] = loan_table.iloc[i,1] - (car_payments - (loan_table.iloc[i,1] * interest))
# We want to round all the values to 2 places
loan_table = loan_table.round(2)

# This command is not necessary.
# It is used to display the entire pandas dataframe
with pd.option_context("display.max_rows",None,"display.max_columns", None):
print(loan_table)``````
``````##    Year  Initial_Balance  Payments  Interest  Principal  Ending_Balance
## 0   1.0         10000.00   2438.91    700.00    1738.91         8261.09
## 1   2.0          8261.09   2438.91    578.28    1860.63         6400.46
## 2   3.0          6400.46   2438.91    448.03    1990.87         4409.59
## 3   4.0          4409.59   2438.91    308.67    2130.24         2279.35
## 4   5.0          2279.35   2438.91    159.55    2279.35            0.00``````

And there you have it, we just built our car loan payment schedule in python. It may seem like too much typing when you compare this with excel (and it is). But the true power of programming is not in such simple calculation (for this excel may be better). But this is very helpful when you are trying run a for loop over millions of items. Python has the ability to perform millions of calculations in fraction of a second.

## Summary

In this post we learned

• To calculate the car payments using the np.pmt() function
• To create an empty dataframe
• To run a for loop
• To build car loan payment