Non-linear equations: Loan calculation

You borrowed $3,000 and are required to pay off the loan in 12 months. If your monthly payment is $265, how much will the interest rate be?
/* Loan calculation */
VAR p = 3000   "Amount of money borrowed   [$]"
    ,n= 12     "Number of months [mon]"
    ,r         "Monthly interest rate   [%/mon]"
    ,x = 265   "Monthly payment  [$/mon]"

eq: p = x * ( 1 - (1+r/100)^(-n) ) / (r/100)

RESET r#0.5[0,2] BY eq

OUTPUT p, x, n, r
Explanation

The equation that must be solved to obtain the monthly interest rate r is non-linear.

The iterative method is specified for calculations in the RESET statement. r, 0.5 and 0-2 are specified for variables, an initial estimate value and the equation to check the convergence, respectively.

/ is used to represent division.

Enter equations and click on the [Solve] button.

/* Loan calculation */ VAR p = 3000 "Amount of money borrowed [$]" ,n= 12 "Number of months [mon]" ,r "Monthly interest rate [%/mon]" ,x = 265 "Monthly payment [$/mon]" eq: p = x * ( 1 - (1+r/100)^(-n) ) / (r/100) RESET r#0.5[0,2] BY eq OUTPUT p, x, n, r

Sample problem

The following sample problems will help you understand how EQUATRAN-G works.

Linear equations: Tsuru-Kame-Zan (Japanese traditional problem, means problem of cranes and tortoises); Nutrients problem
Non-linear equations: Root of 3rd order polynomial equation; Loan calculation
Ordinary differential equations: 2nd order ordinary differential equation
Optimization and least square problems: Approximation in 3rd order polynomial equation