Assignment: Amortization and Rolling Window
Statistics
Professor Ahmad Namini
Python and Applications to Business Analytics
Python and Applications to Finannce
Exercise 1. Amortization
Amortization is a method of repaying a loan through regular payments of interest and principal. The size of the loan (the original balance) is reduced by the principal part of the
payment. The interest part of the payment pays the interest incurred on the remaining
principal balance. As the principal gets paid down over the term of the loan, the interest
part of the payment diminishes.
A new loan is typically issued with the following metrics:
ˆ Principal: amount of the loan
ˆ Interest Rate: annual interest rate
ˆ Term: amount of time to pay back the loan with monthly payments
For instance, a given 15-year $250,000 at an 8.0% interest rate, the monthly payment of
$2,389.13 is expected over the 180 (15 years * 12 payments per year) payments. An online
calculator exists to verify this calculation.
Please note that borrowers have the option to make an extra payment which will be applied to the principal. Extra payments will lower the principal and thus the loan can be paid
in full earlier than expected. A typical payment schedule with no extra payment is seen in
the following.
Month Begin P Payment Interest Extra Payment
1
250,000.00 2,389.13
1,666.66
0.00
2
249,277.53 2,389.13
1,661.85
0.00
3
248,550.25 2,389.13
1,657.00
0.00
ˆ
ˆ
ˆ
ˆ
ˆ
178
7,072.94
2,389.13
47.15
0.00
179
4,730.97
2,389.13
31.53
0.00
180
2,373.38
2,389.13
15.82
0.00
Total
ˆ
430,043.44 180,043.43
Write a Python computer program to do the following:
1
P Applied
722.46
727.27
732.12
ˆ
2,341.97
2,357.59
2,373.30
250,000.00
End P
249,277.53
248,550.25
247,818.12
ˆ
4,730.97
2,373.38
0.00
ˆ
ˆ Get user input of principal, minimum expected payment, interest, and extra payment,
and error check that all input is valid. If not valid, have the user re-enter. Note that
one does not need to enter the term of the loan.
ˆ Compute and print the schedule of payments, similar to the table shown above.
ˆ Compute and print the total (sum of all) payments, interest paid, and principal applied.
ˆ Compute and print the total time (in years) required to payoff the loan.
The computer program should leverage comments, readability, and above all, efficiency.
Please note that I have attached a spreadsheet that computes the payment schedule. The
spreadsheet will greatly enhance your ability to code the solution by understanding the
nature of calculations.
Exercise 2. Rolling Window Statistics
Attached is a file containing named GOOG.csv which has daily market prices over one
year. With the data, compute a rolling window statistics with the statistics being:
ˆ Min, Max, and Mean
ˆ Bollinger Bands: Mean +/- 2.0 * Standard Deviation
Write a Python computer program to do the following:
ˆ From the user, input the rolling window size. For instance, inputting 5 would yield a
weekly window, 20 would be a monthly window, etc. Make sure that the input is valid.
For instance, if a user inputs 400 but the time series only has 250 daily prices, this is
not valid input.
ˆ Over the rolling window size, compute the statistics mentioned above.
Attached also is a file named read file.py for reading data from a file.
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