Description Finally, let's add to our calculator the capacity to compute differentiated payments. We’ll do this for the type of repayment where the loan principal is reduced by a constant amount each month. The rest of the monthly payment goes toward interest repayment and it is gradually reduced over the term of the loan. This means that the payment is different each month. Let’s look at the formula:
n P +i∗(P− n P∗(m−1) )
Where:
D_mD m = mmth differentiated payment;
PP = the loan principal;
ii = nominal interest rate. This is usually 1/12 of the annual interest rate and is a float value, not a percentage. For example, if our annual interest rate = 12%, then i = 0.01.
nn = number of payments. This is usually the number of months in which repayments will be made.
mm = current repayment month.
In this stage, the user has to input a lot of parameters, so it might be convenient to use command-line arguments. The argparse module can help you parse them. You can run your loan calculator via command line like this:
python creditcalc.py Using command-line arguments you can run your program this way:
python creditcalc.py --type=diff --principal=1000000 --periods=10 --interest=10 Check the description and examples below for more details.
Objectives In this stage, you are going to implement the following features:
Calculation of differentiated payments. To do this, the user can run the program specifying interest, number of monthly payments, and loan principal. Ability to calculate the same values as in the previous stage for annuity payment (principal, number of monthly payments, and monthly payment amount). The user specifies all the known parameters with command-line arguments, and one parameter will be unknown. This is the value the user wants to calculate. Handling of invalid parameters. It's a good idea to show an error message if the user enters invalid parameters (they are discussed in detail below). The final version of your program is supposed to work from the command line and parse the following parameters:
--type indicates the type of payment: "annuity" or "diff" (differentiated). If --type is specified neither as "annuity" nor as "diff" or not specified at all, show the error message.
python creditcalc.py --principal=1000000 --periods=60 --interest=10 Incorrect parameters --payment is the monthly payment amount. For --type=diff, the payment is different each month, so we can't calculate months or principal, therefore a combination with --payment is invalid, too: python creditcalc.py --type=diff --principal=1000000 --interest=10 --payment=100000 Incorrect parameters --principal is used for calculations of both types of payment. You can get its value if you know the interest, annuity payment, and number of months. --periods denotes the number of months needed to repay the loan. It's calculated based on the interest, annuity payment, and principal. --interest is specified without a percent sign. Note that it can accept a floating-point value. Our loan calculator can't calculate the interest, so it must always be provided. These parameters are incorrect because --interest is missing: python creditcalc.py --type=annuity --principal=100000 --payment=10400 --periods=8 Incorrect parameters You may have noticed that for differentiated payments you will need 4 out of 5 parameters (excluding payment), and the same is true for annuity payments (the user will be calculating the number of payments, the payment amount, or the loan principal). Thus, you should also display an error message when fewer than four parameters are provided:
python creditcalc.py --type=annuity --principal=1000000 --payment=104000 Incorrect parameters You should also display an error message when negative values are entered:
python creditcalc.py --type=diff --principal=30000 --periods=-14 --interest=10 Incorrect parameters The only thing left is to compute the overpayment: the amount of interest paid over the whole term of the loan. Voila: you have a real loan calculator!
Examples The greater-than symbol followed by a space (> ) represents the user input. Note that this is not part of the input.
Example 1: calculating differentiated payments
python creditcalc.py --type=diff --principal=1000000 --periods=10 --interest=10 Month 1: payment is 108334 Month 2: payment is 107500 Month 3: payment is 106667 Month 4: payment is 105834 Month 5: payment is 105000 Month 6: payment is 104167 Month 7: payment is 103334 Month 8: payment is 102500 Month 9: payment is 101667 Month 10: payment is 100834
Overpayment = 45837 In this example, the user wants to take a loan with differentiated payments. You know the principal, the count of periods, and interest, which are 1,000,000, 10 months, and 10%, respectively.
The calculator should calculate payments for all 10 months. Let’s look at the formula above. In this case:
P = 1000000P=1000000 n = 10n=10 i = \dfrac{ interest }{ 12 * 100% } = \dfrac { 10% }{12 * 100% } = 0.008333...i= 12∗100% interest
12∗100% 10% =0.008333...
Now let’s calculate the payment for the first month:
D_1 = \dfrac{P}{n} + i * \left(P - \dfrac{ P * (m-1) }{ n } \right)=\dfrac{ 1000000 }{ 10 } + 0.008333... * \left( 1000000 - \dfrac{ 1000000*(1-1) }{ 10 } \right) = 108333.333...D 1
n P +i∗(P− n P∗(m−1) )= 10 1000000 +0.008333...∗(1000000− 10 1000000∗(1−1) )=108333.333...
The second month (m = 2m=2):
D_2 = \dfrac{P}{n} + i * \left(P - \dfrac{ P * (m-1) }{ n } \right)=\dfrac{ 1000000 }{ 10 } + 0.008333... * \left( 1000000 - \dfrac{ 1000000*(2-1) }{ 10 } \right) = 107500D 2
n P +i∗(P− n P∗(m−1) )= 10 1000000 +0.008333...∗(1000000− 10 1000000∗(2−1) )=107500
The third month (m = 3m=3):
D_3 = \dfrac{P}{n} + i * \left(P - \dfrac{ P * (m-1) }{ n } \right)=\dfrac{ 1000000 }{ 10 } + 0.008333... * \left( 1000000 - \dfrac{ 1000000*(3-1) }{ 10 } \right) = 106666.666...D 3
n P +i∗(P− n P∗(m−1) )= 10 1000000 +0.008333...∗(1000000− 10 1000000∗(3−1) )=106666.666...
And so on. You can see other monthly payments above.
Your loan calculator should output monthly payments for every month as in the first stage. Also, round up all floating-point values. Finally, your loan calculator should add up all the payments and subtract the loan principal so that you get the overpayment.
Example 2: calculate the annuity payment for a 60-month (5-year) loan with a principal amount of 1,000,000 at 10% interest
python creditcalc.py --type=annuity --principal=1000000 --periods=60 --interest=10 Your annuity payment = 21248! Overpayment = 274880 Example 3: fewer than four arguments are given
python creditcalc.py --type=diff --principal=1000000 --payment=104000 Incorrect parameters. Example 4: calculate differentiated payments given a principal of 500,000 over 8 months at an interest rate of 7.8%
python creditcalc.py --type=diff --principal=500000 --periods=8 --interest=7.8 Month 1: payment is 65750 Month 2: payment is 65344 Month 3: payment is 64938 Month 4: payment is 64532 Month 5: payment is 64125 Month 6: payment is 63719 Month 7: payment is 63313 Month 8: payment is 62907
Overpayment = 14628 Example 5: calculate the principal for a user paying 8,722 per month for 120 months (10 years) at 5.6% interest
python creditcalc.py --type=annuity --payment=8722 --periods=120 --interest=5.6 Your loan principal = 800018! Overpayment = 246622 Example 6: calculate how long it will take to repay a loan with 500,000 principal, monthly payment of 23,000, and 7.8% interest
python creditcalc.py --type=annuity --principal=500000 --payment=23000 --interest=7.8 It will take 2 years to repay this loan! Overpayment = 52000