Problem Statement: The follwing formula relates payment per period, interest rate, and principal of a loan/annuity.
payment = P * r / (1-1/(1+r)N)
where payment = equal monthly payment
P = original principal
r = interest rate per payment period
N = number of payment period
Suppose you obtain from a bank a 3-year loan of $12,000 to
purchase a car at an annual percentage rate (APR) of 9%. The
loan is to be paid back in equal monthly installments. Write a
program to find the equal monthly payment, the
total interest and principal payments, and print out a repayment
table resembling the following.
-------------------------------------------------------
Month Interest-Paid Principal-Paid Balance
-------------------------------------------------------
0 0.00 0.00 12000.00
1 90.00 291.60 11708.43
: : : :
36 2.84 378.63 0.00
-------------------------------------------------------
Total 13737.47 12000.00 0.00
Extra Credits Only.
Since, $0.01 is the lowest US currency denomination and you
cannot transact a fraction of a penny in practice, add steps to
round off the monthly payment to the nearest penny. Because of
the round-off, the last payment is usually different from the
rest by a few pennies to make the last balance come out to 0.
Note: Mathcad v5.0 provides a function "floor(x)" to truncate a
real number x and "ceil(x)" to push up a real number x to the
next integer. (e.g., floor(3.3)=3 & ceil(3.3)=4). In addition,
Mathcad provides a modulus (remainder) function "mod(x,y)" (e.g.,
mod(5,3)=2). You may find these inter-related functions to be
useful in defining a round-off function "round(x)".
Solution:
Problem Statement: Solve the above problem (the monthly payment problem). Specifically, you should write a function that returns the balance at the end of specified number of payment periods. Allow both positive and negative balances. You should provide a main program that read/set the original principal, annual interest rate, and the number of monthly payments to be made. Call a subroutine that solves an equation of the form f(x)=0 to find the fixed, equal monthly payment. After you find the monthly payment, print out a table of payment schedule.
Test case: You will find this program to be very useful in managing your personal finance. You test the program with the tuition loan from the last quiz or any type of loan (car loan or home mortgage). Suppose you obtain from a bank a 3-year loan of $12,000 to purchase a car at an annual percentage rate (APR) of 9%. The loan is to be paid back in equal monthly installments. Write a program to find the equal monthly payment, the total interest and principal payments, and print out a repayment table resembling the following.
-------------------------------------------------------
Month Interest-Paid Principal-Paid Balance
-------------------------------------------------------
0 0.00 0.00 12000.00
1 90.00 291.60 11708.43
: : : :
36 2.84 378.63 0.00
-------------------------------------------------------
Total 13737.47 12000.00 0.00
There exists a "fancy" formula to calculate the monthly payment,
but I do not want you to use it because I want you to practice
putting a given problem in the standard "f(x)=0" form. The
"fancy" formula you will learn in ENCH444 (Process Engineering
Economics and Design), which you might want to use as an
analytical reference to check your numerical result, is:
payment = P * r / (1-1/(1+r)N)
where payment = equal monthly payment
P = original principal
r = interest rate per payment period
N = number of payment periods
Extra Credits Only. Since, $0.01 is the lowest US currency denomination and you cannot transact a fraction of a penny in practice, add steps to round off the monthly payment to the nearest penny. Because of the round-off, the very last payment is usually different from the rest by a few pennies to make the last balance come out to exactly 0. Furthermore, since you get only ~7 significant digits with the regular, single precision real variable in FORTRAN, a program written in single precision may miss a few pennies when the loan amount is, say $1,000,000.00. Since you may one day be able to afford a million dollar house; you may want to write your program in double precision real variables to handle accurately a large number.
Solution:
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