declare
  m       number := 100000; --pv
  p       number := 830.33; --pmt
  n       number := 15; --nper
  n12     number := 12 * n;
  pm      number := p / m;
  i       number := pm;
  old_i   number := 2 * pm;
  ret_val number;
  cnt     pls_integer := 0;
begin
--  while old_i > i                    /* to compute to maximum precision */
  while old_i - i > 5 * power(10,-11)  /* to achieve 10 digits precision */
  loop
    cnt := cnt + 1;
    old_i := i;
    i := pm * (1 - 1 / power(1 + i,n12));
    if cnt > 500 then
      exit;
    end if;
    dbms_output.put_line(to_char(cnt)||' '||to_char(old_i)||' '||to_char(i)||' '||to_char(old_i - i));
  end loop;
  ret_val := 12 * i;
  dbms_output.put_line(to_char(cnt)||' iterations to return '||to_char(ret_val));
end;

DECLARE 
    m       NUMBER := 100000; --pv 
    p       NUMBER := 830.33; --pmt 
    n       NUMBER := 15; --nper 
    n12     NUMBER := 12 * n; 
    pm      NUMBER := p / m; 
    i       NUMBER := pm; 
    old_i   NUMBER := 2 * pm; 
    ret_val NUMBER; 
    cnt     PLS_INTEGER := 0; 
BEGIN 
    --  while old_i > i                    /* to compute to maximum precision */ 
    WHILE old_i - i > 5 * Power(10, -11) /* to achieve 10 digits precision */ 
    LOOP 
        cnt := cnt + 1; 

        old_i := i; 

        i := pm * ( 1 - 1 / Power(1 + i, n12) ); 

        IF cnt > 500 THEN 
          EXIT; 
        END IF; 

        dbms_output.Put_line(To_char(cnt) 
                             ||' ' 
                             ||To_char(old_i) 
                             ||' ' 
                             ||To_char(i) 
                             ||' ' 
                             ||To_char(old_i - i)); 
    END LOOP; 

    ret_val := 12 * i; 

    dbms_output.Put_line(To_char(cnt) 
                         ||' iterations to return ' 
                         ||To_char(ret_val)); 
END; 

CREATE OR REPLACE FUNCTION RATE (pv IN number, fv IN number, pmt IN number, nper IN number, type IN number )
    RETURN number IS rate number;
BEGIN
	DECLARE
		guess NUMBER(6,3) := .1;
		rate BINARY_DOUBLE;
		FINANCIAL_MAX_ITERATIONS NUMBER(10) := 100;
		FINANCIAL_PRECISION BINARY_DOUBLE := .000001;
		y BINARY_DOUBLE;
		y0 BINARY_DOUBLE;
		y1 BINARY_DOUBLE;
		f BINARY_DOUBLE;
		i NUMBER(10);
		x0 BINARY_DOUBLE := 0;
		x1 BINARY_DOUBLE;
BEGIN
	rate := guess;
IF(ABS(rate) < FINANCIAL_PRECISION) THEN y := pv * (1 + nper * rate) + pmt * (1 + rate * type) * nper + fv;
									ELSE
										f := EXP(nper * LN(1 + rate));
										y := pv * f + pmt * (1 / rate + type) * (f - 1) + fv;
									END IF;

y0 := pv + pmt * nper + fv;
y1 := pv * f + pmt * (1 / rate + type) * (f - 1) + fv;

i  := x0 ;
x1 := rate;

WHILE ((ABS(y0 - y1) > FINANCIAL_PRECISION) AND (i < FINANCIAL_MAX_ITERATIONS)) 
LOOP
    rate := (y1 * x0 - y0 * x1) / (y1 - y0);
    x0 := x1;
    x1 := rate;

    IF (ABS(rate) < FINANCIAL_PRECISION) THEN 	y := pv * (1 + nper * rate) + pmt * (1 + rate * type) * nper + fv;
										 ELSE 
												f := EXP(nper * LN(1 + rate));
												y := pv * f + pmt * (1 / rate + type) * (f - 1) + fv;
										 END IF;

    y0 := y1;
    y1 := y;
    i := i + 1;
END LOOP;
RETURN RATE;
END;
END;

select rate(10053.96,  -9457.25, -124.38, 6, 1)*100 FROM DUAL; --%FORMAT
select rate(10053.96,  -9457.25, -124.38, 6, 1)*12*100 FROM DUAL;-- ANNUAL RATE (X12) IN %FORMAT

RETURN RATE;

Nan

CREATE OR REPLACE FUNCTION rate
  (nper  IN NUMBER, 
   pmt   IN NUMBER, 
   pv    IN NUMBER, 
   fv    IN NUMBER DEFAULT  0, 
   type  IN NUMBER DEFAULT  0,
   guess IN NUMBER DEFAULT .1)   
  RETURN    NUMBER 
AS 
  rate                     BINARY_DOUBLE;
  financial_max_iterations NUMBER(10) := 100;
  financial_precision      BINARY_DOUBLE := .000001;
  y                        BINARY_DOUBLE;
  y0                       BINARY_DOUBLE;
  y1                       BINARY_DOUBLE;
  f                        BINARY_DOUBLE;
  i                        NUMBER(10);
  x0                       BINARY_DOUBLE := 0;
  x1                       BINARY_DOUBLE;
BEGIN
  rate := guess;
  IF (ABS(rate) < financial_precision)
    THEN y := pv * (1 + nper * rate) + pmt * (1 + rate * type) * nper + fv;
  ELSE
    f := EXP(nper * LN(1 + rate));
    y := pv * f + pmt * (1 / rate + type) * (f - 1) + fv;
  END IF;
  y0 := pv + pmt * nper + fv;
  y1 := pv * f + pmt * (1 / rate + type) * (f - 1) + fv;
  i  := x0 ;
  x1 := rate;
  WHILE ((ABS(y0 - y1) > FINANCIAL_PRECISION) AND (i < FINANCIAL_MAX_ITERATIONS)) 
  LOOP
    rate := (y1 * x0 - y0 * x1) / (y1 - y0);
    x0 := x1;
    x1 := rate;
    IF (ABS(rate) < FINANCIAL_PRECISION) 
      THEN y := pv * (1 + nper * rate) + pmt * (1 + rate * type) * nper + fv;
    ELSE 
      f := EXP(nper * LN(1 + rate));
      y := pv * f + pmt * (1 / rate + type) * (f - 1) + fv;
    END IF;
    y0 := y1;
    y1 := y;
    i := i + 1;
  END LOOP;
  RETURN rate;
END rate;
/

SCOTT@orcl_12.1.0.2.0> CREATE OR REPLACE FUNCTION rate
  2    (nper  IN NUMBER,
  3  	pmt   IN NUMBER,
  4  	pv    IN NUMBER,
  5  	fv    IN NUMBER DEFAULT  0,
  6  	type  IN NUMBER DEFAULT  0,
  7  	guess IN NUMBER DEFAULT .1)
  8    RETURN	 NUMBER
  9  AS
 10    rate			BINARY_DOUBLE;
 11    financial_max_iterations NUMBER(10) := 100;
 12    financial_precision	BINARY_DOUBLE := .000001;
 13    y			BINARY_DOUBLE;
 14    y0			BINARY_DOUBLE;
 15    y1			BINARY_DOUBLE;
 16    f			BINARY_DOUBLE;
 17    i			NUMBER(10);
 18    x0			BINARY_DOUBLE := 0;
 19    x1			BINARY_DOUBLE;
 20  BEGIN
 21    rate := guess;
 22    IF (ABS(rate) < financial_precision)
 23  	 THEN y := pv * (1 + nper * rate) + pmt * (1 + rate * type) * nper + fv;
 24    ELSE
 25  	 f := EXP(nper * LN(1 + rate));
 26  	 y := pv * f + pmt * (1 / rate + type) * (f - 1) + fv;
 27    END IF;
 28    y0 := pv + pmt * nper + fv;
 29    y1 := pv * f + pmt * (1 / rate + type) * (f - 1) + fv;
 30    i  := x0 ;
 31    x1 := rate;
 32    WHILE ((ABS(y0 - y1) > FINANCIAL_PRECISION) AND (i < FINANCIAL_MAX_ITERATIONS))
 33    LOOP
 34  	 rate := (y1 * x0 - y0 * x1) / (y1 - y0);
 35  	 x0 := x1;
 36  	 x1 := rate;
 37  	 IF (ABS(rate) < FINANCIAL_PRECISION)
 38  	   THEN y := pv * (1 + nper * rate) + pmt * (1 + rate * type) * nper + fv;
 39  	 ELSE
 40  	   f := EXP(nper * LN(1 + rate));
 41  	   y := pv * f + pmt * (1 / rate + type) * (f - 1) + fv;
 42  	 END IF;
 43  	 y0 := y1;
 44  	 y1 := y;
 45  	 i := i + 1;
 46    END LOOP;
 47    RETURN rate;
 48  END rate;
 49  /

Function created.

SCOTT@orcl_12.1.0.2.0> SHOW ERRORS
No errors.
SCOTT@orcl_12.1.0.2.0> SELECT rate (4*12, -200, 8000) * 100 FROM DUAL
  2  /

RATE(4*12,-200,8000)*100
------------------------
              .770147249

1 row selected.

SCOTT@orcl_12.1.0.2.0> SELECT rate (6, -124.38, 10053.96) * 100 FROM DUAL
  2  /

RATE(6,-124.38,10053.96)*100
----------------------------
                   -45.38631

1 row selected.

SCOTT@orcl_12.1.0.2.0> SELECT rate (6, -124.38, 10053.96, -9457.25) * 100 FROM DUAL
  2  /

RATE(6,-124.38,10053.96,-9457.25)*100
-------------------------------------
                           .254213362

1 row selected.

SCOTT@orcl_12.1.0.2.0> SELECT rate (6, -124.38, 10053.96, -9457.25, 1) * 100 FROM DUAL
  2  /

RATE(6,-124.38,10053.96,-9457.25,1)*100
---------------------------------------
                             .257478973

1 row selected.

CREATE OR REPLACE FUNCTION fnc_g_div_gp(r in number, n in number, p in number, x in number, y in number, w in number)
    return number                    
    is

   /* Evaluate g(r_n)/g'(r_n), where g := fv + pv*(1+rate)**nper + pmt*(1+rate*when)/rate * ((1+rate)**nper - 1)*/
   
     t1  number;
     t2  number;
     g  number;
     gp  number;
     res  number;
 
   begin
     

    t1 := power((r+1),n);
    t2 := power((r+1),(n-1));
    g := y + t1 * x + p * (t1 - 1) * (r * w + 1) / r;
    gp := (n * t2 * x - p * (t1 - 1) * (r * w + 1) / (power(r,2)) + n * p * t2 * (r * w + 1) / r + p * (t1 - 1) * w/ r);
    res := g / gp;
 
   return res;
     
  end;

with function fnc_getRate(nper in number, pmt in number, pv in number, fv in number, type_ in number)
    return number                  
    is

   /* Evaluate g(r_n)/g'(r_n), where g := fv + pv*(1+rate)**nper + pmt*(1+rate*when)/rate * ((1+rate)**nper - 1)*/
 begin
    declare
        guess number(6,3) := .5;
        rate number;
        maxiter number(10) := 100;
        tol number := .000001;
        close_ number := 0;
        
        iterator  number;
        rn  number;
        rnp1  number;
        diff  number;
        g  number;
 
   begin
     
    rn := guess;
 	iterator := 0;
 	while (iterator < maxiter)
        loop
            rnp1 := rn - fnc_g_div_gp(rn, nper, pmt, pv, fv, type_);
            diff := abs(rnp1 - rn);
            iterator := iterator + 1;
            rn := rnp1;
        end loop;
 	return rn;
   end;
end;

select fnc_getRate(36,749,-2531,0,0) as rate from dual
;