Loan Structuring

Develop a program to find EMI (Equated Monthly Installment) and the amortization schedule for loan repayment. Three primary inputs for doing loan arithmetic are Loan Amount, Rate of interest and Tenure. Rate of interest can vary over certain months and affect the tenure. Write a program to calculate EMI, total interest paid over entire tenure of the loan and amortization schedule. Amortization schedule is explained in text below.
This problem will take into account frequency of payment viz. MONTHLY/YEARLY/ DAILY. The EMI is payable at this frequency. The interest rate variation is captured in form of From Installment number to To Installment number. The interest rate may vary or may remain constant over the tenure of the loan repayment schedule.
Program should accept name of the file as input on console. The file will contain inputs such as loan amount, rate etc. See details in input specification section below. In case of a bad input, program should notify user with invalid input.

Information:

·                  EMI are the payments one makes in order to pay off the loan. On a specific date every month,one needs to pay the EMI. EMI depends upon loan amount, interest rate, loan tenure and the frequency in which one wants to pay EMI i.e can be monthly/quarterly/yearly etc

·                  Round off the interest paid to the nearest rupee.

·                  EMI can be calculated using the formula:

EMI = (L*I)* {((1+I)^N) / ([(1+I)^N]-1)}

where
L = loan amount
I = interest Rate(rate per annum divided by 12)
^ = to the power of
N = Loan Period in months

Example

Mr. Gonsalves borrowed Rs 57,00,000 Lakhs (Rs 5.7 million) at 10% per annum for a tenure of 20 years with EMI payable monthly. According to his loan plan after 100 months for next 50 months, the rate of interest changes to 10.5.

So here, Loan amount=Rs 57,00,000 Lakhs (Rs 5.7 million) 
Rate of interest= 10
Tenure=240(20*12)
Frequency=MONTHLY
From Installment:100
To Installment:150
Rate of interest= 10.5

EMI calculated, using formula mentioned above is 55006.23376921851. Rounded off to two digits after decimal point, EMI becomes Rs 55006.23. Amortization schedule for this loan case looks similar to the table shown below :

Amortization Schedule:

InstNo.	Opening Principal	Installment Amount	Principal Component	Interest Component	Closing Principal	Rate Of Interest
1	5700000	55006.23	7506.23	47500	5692493.77	10
2	5692493.77	55006.23	7568.79	47437.45	5684924.98	10
3	5684924.98	55006.23	7631.86	47374.37	5677293.12	10
4	...	...	...	...	...
5
99	4569291.63	55006.23	16928.8	38077.43	4552362.83	10
100	4552362.83	55006.23	15173.06	39833.17	4537189.77	10.5
101	4537189.77	55006.23	15305.82	39700.41	4521883.95	10.5
245
246						10.5
247	54551.64	55006.23	54551.64	454.6	0	10.5

Total interest paid on 57,00,000 at rate 10.50 is 78,77,467.47 in 247 installments. While printing the output report interest paid rounded off to the nearest multiple of hundered (100). In this case it will be 78,77,500 .Refer section on Output Format for precise instructions.

Note, two things from the table and the sentence above

1.               Since the rate of change of interest is marked from 100^th month to 150^th month, but no additional information is provided about the rate from 151^st month till the end of the tenure. Hence rate of interest in this case will remain as 10.5 until any explicit rate change, to take place later is provided. In this case, since no information is provided, rate will remain 10.5% until end of tenure.

2.               At the start of the problem, it was stated that the tenure is 240 months. But due to increase in rate of interest and no change in EMI, the tenure increased to 247 months. You are assured that rate of interest will never change in such a way that with the current EMI amount the loan can never be repaid. Such test cases are out of scope for this problem.

Input Format

Line 1	Name of the file from which inputs are to be taken. The input file format is described next.
Line 2	A particular installment number whose opening principle is to be calculated using amortization schedule.

Note:
The Input in file column in table below on Sample Test Cases is provided to help you visualize how the input file will look like.

File Format

Line 1	Loan Amount (L)
Line 2	Rate of Interest per annum (R) in percentage
Line 3	Tenure (N)
Line 4	Frequency of payment Frequency can be MONTHLY/YEARLY/DAILY for MONTHLY Rate of Interest =Rate of Interest per annum (R) /12 DAILY Rate of Interest=Rate of Interest per annum (R)/365
If there is a change of rate of interest then following lines will be a part of the input
Line 5	From installment
Line 6	To installment
Line 7	Changed Rate of Interest

Constraints

1.               Here:

0 <= L <= 10,000,000,000

0 <= R <= 100

1 <= N <= 1188

2.               In case of change of rate of interest, the To installment value should be greater than From installment value

Output Format

Line 1	For valid input,print EMI amount rounded to 2 digits after decimal point For Invalid input,print Invalid Input
Line 2	For valid input,print Opening Principal before installment X is Rs Y where X is the input provided in Line 2 (installment number) and Y is Prinicipal outstanding in Rs rounded to nearest multiple of hundered (100) For Invalid input,print Please Mention Frequency Of EMI As MONTHLY/YEARLY/DAILY
Line 3	Interest paid is Rs Z where Z = interest paid over entire tenure rounded to nearest multiple of hundered (100)

Sample Input and Output

SR.no	Input	Input in File	Output
1	EMIinput.txt 25	15000 10.5 240 MONTHLY  200 220 11 221 240 12	EMI is Rs 149.76 Opening Principal before installment 25 is Rs 14500 Interest paid is Rs 21000
2	EMIinput.txt 23	1000 10 25 abc	Invalid Input Please Mention Frequency Of EMI As MONTHLY/YEARLY/DAILY
3	EMIinput.txt 11	5 25 40 DAILY ??	Invalid Input
4	EMIinput.txt 12	1200000 25  40 DAILY	EMI is Rs 30423.11 Opening Principal before installment 12 is Rs 873300 Interest paid is Rs 16900